ipynb • Lines: 939{
"cells": [
{
"cell_type": "markdown",
"id": "bb5afc1a",
"metadata": {},
"source": [
"# Lab: Central Limit Theorem\n",
"\n",
"Welcome! In this ungraded lab see applications of the Central Limit Theorem when working with different distributions of data. You will see how to see the theorem in action, as well as scenarios in which the theorem doesn't hold.\n",
"\n",
"Let's get started!"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "dff173ef",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"from scipy import stats\n",
"from scipy.stats import norm\n",
"\n",
"import utils"
]
},
{
"cell_type": "markdown",
"id": "c4298763",
"metadata": {},
"source": [
"## Gaussian population\n",
"\n",
"Begin with the most straightforward scenario: when your population follows a Gaussian distribution. You will generate the data for this population by using the [np.random.normal](https://numpy.org/doc/stable/reference/random/generated/numpy.random.normal.html) function. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "db0e6232",
"metadata": {},
"outputs": [],
"source": [
"mu = 10\n",
"sigma = 5\n",
"\n",
"gaussian_population = np.random.normal(mu, sigma, 100_000)"
]
},
{
"cell_type": "markdown",
"id": "2bafe463",
"metadata": {},
"source": [
"The population has a mean of 10 and a standard deviation of 5 (since these are the true parameters you used to generate the data) and a total of 100'000 observations. You can visualize its histogram by running the next cell:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "aa13b407",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.histplot(gaussian_population, stat=\"density\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "7dffb432",
"metadata": {},
"source": [
"## Sampling from the population\n",
"\n",
"Since this lab uses simulated data you could very easily use the whole population to draw conclusions from the data. For instance if you didn't know about the values of $\\mu$ and $\\sigma$ you could get very close estimates of the true values by computing the mean and standard deviation of the whole population like so:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "d77f1985",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Gaussian population has mean: 10.0 and std: 5.0\n"
]
}
],
"source": [
"gaussian_pop_mean = np.mean(gaussian_population)\n",
"gaussian_pop_std = np.std(gaussian_population)\n",
"\n",
"print(f\"Gaussian population has mean: {gaussian_pop_mean:.1f} and std: {gaussian_pop_std:.1f}\")"
]
},
{
"cell_type": "markdown",
"id": "774ec0e3",
"metadata": {},
"source": [
"However in real life this will most certainly not be possible and you will need to use samples that are nowhere near as big as the population to draw conclusions of the behaviour of the data. After all, this is what statistics is all about.\n",
"\n",
"Depending on the sampling techniques you could encounter different properties, this is where the Central Limit Theorem comes in handy. For many distributions (**but not all**) the following is true:\n",
"\n",
"The sum or average of a large number of independent and identically distributed random variables tends to follow a normal distribution, regardless of the distribution of the individual variables themselves. This is important because the normal distribution is well-understood and allows for statistical inference and hypothesis testing.\n",
"\n",
"With this in mind you need a way of averaging samples out of your population. For this the `sample_means` is defined:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "996fd8ef",
"metadata": {},
"outputs": [],
"source": [
"def sample_means(data, sample_size):\n",
" # Save all the means in a list\n",
" means = []\n",
"\n",
" # For a big number of samples\n",
" # This value does not impact the theorem but how nicely the histograms will look (more samples = better looking)\n",
" for _ in range(10_000):\n",
" # Get a sample of the data WITH replacement\n",
" sample = np.random.choice(data, size=sample_size)\n",
"\n",
" # Save the mean of the sample\n",
" means.append(np.mean(sample))\n",
"\n",
" # Return the means within a numpy array\n",
" return np.array(means)"
]
},
{
"cell_type": "markdown",
"id": "19fec648",
"metadata": {},
"source": [
"Let's break down the function above:\n",
"\n",
"- You take random samples out of the population (the sampling is done with replacement, which means that once you select an element you put it back in the sampling space so you could choose a particular element more than once). This ensures that the independence condition is met.\n",
"\n",
"- Compute the mean of each sample\n",
"\n",
"- Save the means of each sample in a numpy array\n",
"\n",
"The theorem states that if a large enough `sample_size` is used (usually bigger than 30) then the distribution of the sample means should be Gaussian. See it in action by running the next cell:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "07799fb7",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Compute the sample means\n",
"gaussian_sample_means = sample_means(gaussian_population, sample_size=5)\n",
"\n",
"# Plot a histogram of the sample means\n",
"sns.histplot(gaussian_sample_means, stat=\"density\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "e0f7829f",
"metadata": {},
"source": [
"The distribution of the sample means looks pretty Gaussian. However this is not good enough to determine if the theorem holds, after all you used a very small `sample_size` in this example. There are various ways to check if the sample means do follow a Gaussian distribution.\n",
"\n",
"The first one is to compute the theoretical $\\mu$ and $\\sigma$ of the sample means which will be denoted with the symbols $\\mu_{\\bar{X}}$ and $\\sigma_{\\bar{X}}$ respectively. These values can be computed as follows:\n",
"\n",
"- $\\mu_{\\bar{X}} = \\mu$\n",
"\n",
"\n",
"- $\\sigma_{\\bar{X}} = \\frac{\\sigma}{\\sqrt{n}}$\n",
"\n",
"**Note: In this case $n$ is the size of the sample.**\n",
"\n",
"And then use these values to plot a Gaussian curve with parameters $\\mu_{\\bar{X}}$ and $\\sigma_{\\bar{X}}$. If the theorem holds then the resulting distribution of the sample means should resemble this Gaussian curve. Run the next cell to include this into the plot:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "fa1b3ff2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Compute estimated mu\n",
"mu_sample_means = mu\n",
"\n",
"# Compute estimated sigma\n",
"# 5 is being used because you used a sample size of 5\n",
"sigma_sample_means = sigma / np.sqrt(5)\n",
"\n",
"# Define the x-range for the Gaussian curve (this is just for plotting purposes)\n",
"x_range = np.linspace(min(gaussian_sample_means), max(gaussian_sample_means), 100)\n",
"\n",
"# Plot everything together\n",
"sns.histplot(gaussian_sample_means, stat=\"density\")\n",
"plt.plot(\n",
" x_range,\n",
" norm.pdf(x_range, loc=mu_sample_means, scale=sigma_sample_means),\n",
" color=\"black\",\n",
")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "9e33c158",
"metadata": {},
"source": [
"They look pretty similar. However you can go one step further and plot a smooth function that attempts to estimate the probability density function of the sample means through a method known as `kernel density estimation`. If this smooth function resembles the Gaussian function then you know that the distribution of the sample means is very similar to a Gaussian:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a315905d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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99xxQ2Y/qkUceoXPnztxwww107NiRhQsXVpv16aefpk+fPowcOZJhw4YREBDArbfeWl9/NA1Co/z1pmoDKS8vx8XFha+++orbbrvNNv/xxx/nwIEDbNq06ZLrDxs2jF69erFgwYJLtuvevTvR0dG8//77tnlz5szh1VdfxdPTE0dHRwYMGMB//vOfSz7NYDKZMJlMts8FBQWEhISQn5+Ph4fHZY5WCNEcWEvKWNkllrTrxpDd2p+jR3fw/f8qf2EMHnwbESXnef/t+ZSfTKUiLQOfpx5Eo63Zv2FTUlIYNmwYycnJDBgwgK1bt+LgIA90q6WsrIykpCRbt5Wmrri4mDZt2vD6668zadIktePUu0udv4KCAjw9Pev197dqV65ycnKwWCz4+/vbzff396+zy4G7d+/m119/ZfLkyXbzBwwYwPLly1mzZg0ffPABGRkZDBo0iNzc3Itua968eXh6etomGaNGiOZt9O1jiYoZ/sc05Dq+7BpLl2IrGkWhoOAcP6/5CIC+USMZMviPfySW/5ZE3lufkvnQHBRzRY32FxYWxvr16/H09GTXrl3Mnz+/Xo5LtAwJCQl8/vnnnDp1iv3793PvvZVXVMeMGaNyspZB9Q7t1T3NcCUd9y5lyZIldOvWze5xVIBRo0bZxt8YMWIEP/74I1A5QNnFzJo1i/z8fNuUlpZWJxmFEI2TMTuXyPFzbdPYbrfRr0jhA00+ma39WRu/jPLyMoIC23HddffYfW+5jR6K95MPUPzjZjImP1PjAisiIoI33ngDgGeeeYZjx47Vy7GJluG1116jZ8+ejBgxguLiYrZs2UKrVq3UjtUiqFZctWrVCp1OV+UqVVZWVpWrWbVRUlLCihUrqly1qo6rqyvdu3e/5NMJjo6OeHh42E1CiJbBpbiIG1f/j8R27TmoKee333Zz8mQCWq2OUaMmo63m1p/zwJ74PDmJkrXbyXn2nRrva+LEiYwaNQqTycTEiROpqKhZYSbEn/Xu3Zt9+/ZRVFTEuXPniI+Ptw3oKeqfasWVwWAgKiqK+Ph4u/nx8fEMGjToqrf/5ZdfYjKZuO+++y7b1mQycezYMQIDA696v0KI5se5pJScVn7sGjAIs9VC/C/LAYiOvgU/v+CLrufUrxs+sx/iPzvWEzXkOvvbjDHDGX372CrraDQa3n//fTw9Pdm9e7fcHhSiCVK1t2RcXBzjx4+nb9++tk7nqampTJkyBai8FZeens7y5ctt61wYZ6OoqIjs7GwOHDiAwWCgS5cudttesmQJt956K76+vlX2O2PGDG6++WZCQ0PJyspi7ty5FBQUMGHChPo7WCFEk2U26FkbOwqAU0XZlJQV0Mq3DdEDb77suk69O5PzUSHXjXqIkDNpbB80BH6/hZj4339Xu05wcDBvvPEGDzzwAM888ww333zzRR9jF0I0PqoWV+PGjSM3N5fnn38eo9FIt27dWL16NWFhYUDloKF/HfOqd+/etv/ft28fn332GWFhYSQnJ9vmnzhxgq1bt7J27dpq93vmzBnuvvtucnJy8PPzY+DAgezcudO2XyGEAEBRuOmH78j0DyC3lR9JSYfJKCsANIwaNQkHB/1lN3FBx+O/ce2m9ThUVLB56LWXbT9x4kS+/vprVq9ezZQpU9i4cWOd9UcVQtQv1Z/znTp1KlOnTq122Z8HLLugJiNHdOjQ4ZLtVqxYUeN8QoiWq/3JRAbt3M6a628g22rll18+ASAqagRt2kReZm17p9pH4pmfx8i1P3He25vDPXpdsr1Go2Hx4sVERkayefNm1q1bx4gRI2p7KEKIBqT604JCCNEoKQrXx/9MRmt/0kJC+e23XeSeO4uDRss1MX+7/PrV2N+nL4ntI7nz6y8IS066bPsLrw+ByqcHVRqWUAhxhaS4EkKIakQVKQSnn2FfVD+sisK27d8CEOzijaOjc+02qtGwZchQMgICaZ2VWaNVZs6cibOzMzt27ODnn3+u3X6FEA1KiishhKjGqPMWjAGBGIPacPz4bnJzz+Lo6EKws9dVbdeq0/HzyBsxBgahVRQUq/WS7QMCAmxdJ+TqlaiJYcOGMW3atIsu12g0fPvttw2WpyVSvc+VEEI0Rsv8dQzoOxRFsdquWvXrdwMOJ369+o1rNOjNZsaeOMcHHYbxXmDVjvGBfr78sOpLAJ588kkWL17M3r17+eGHH7j55ss/pSjqz+jbx2LMvvgbPeran/8u1AWj0VijF4tDZSH2zTffNPl3/TU0Ka6EEOIvLHkFuFqg0MOT47/tIicnHUdHF/pGxXKgLoqr3+WhcHu+Qs7IOzjUs7fdsj8P0+Dn58ejjz7KSy+9xDPPPMNNN91U7cClomFcGL2/oVxsyI7aCggIqNPtiarkp1MIIf7EdPA4Kd1vp41Jqbxqte1bAPr2HYmTk2ud7ms7ZSS2a8+t367C+9ylr4TMmDEDd3d3Dhw4ILd0xGVZrVaeeOIJfHx8CAgIYM6cObZlf74tWF5ezj/+8Q8CAwNxcnIiPDycefPmARAeHg7AbbfdhkajsX0WlyfFlRBC/Mn5tz9F6+VOlh5OnNhHds4ZHA3O9Os7su53poHtg2Ioc3Jk3BefobVYLtrU19fX1o/m+eefl75X4pI+/vhjXF1d2bVrF6+88grPP/98lTeiALz11lt8//33fPnllxw/fpxPPvnEVkTt2bMHgKVLl2I0Gm2fxeVJcSWEEL8zp5yl+H+bcLvlWizA9h3fAxAVFVvnV61s+zQY2Dj0OvI8vdBdorgCmD59Os7Ozhw8eJBt27bVSx7RPPTo0YNnn32WyMhI7r//fvr27cu6deuqtEtNTSUyMpIhQ4YQFhbGkCFDuPvuu4HK29EAXl5eBAQE2D6Ly5PiSgghfpf//tdo3VxwHj6AnJICMjOTcXDQ069fPVy1+pPs1v7sGjgIvdkMl7gi5e3tzT333APAu+++W6+ZRNPWo0cPu8+BgYFkZWVVaTdx4kQOHDhAx44deeyxxy76ZhNxZaRDuxBCUPn2B3OaEZcbBqN1NJCYcxaATp0G4OzsXqNtGM+m89CjcVXnZ2Ry8dc7/6Hf7p20TTrFxxMmXbTNI488wpIlS1i5ciUZGRnSOVlUS6+3fwJVo9FgrWbYjz59+pCUlMRPP/3EL7/8wtixYxkxYgRff/11Q0VtlqS4EkIIKn/5+MycjCU3j9z8PJLPV/4rv0/v4TXehkXREBxbtTA6s/SFGq1f6uxM29OniN6xleMXadO7d2+io6PZsWMHH3zwAU8//XSN8wlRHQ8PD8aNG8e4ceO48847ueGGGzh37hw+Pj7o9Xosl7ldLaqS24JCiBZPKTdT9L9NWHLy0Gi1fLL6f1gVBX//MAID2zVYjuzW/hzr3JURv8Tja7747cFHHnkEgPfee4+KioqGiieaoTfeeIMVK1bw22+/ceLECb766isCAgLw8vICKp8YXLduHRkZGZw/f17dsE2IFFdCiBav6IdNZD7wbyrSM7FarXz4XeUtkd69rkOj0TRolr1RfTHrHZiYefGi6c4776R169akp6fz3XffNWA60dy4ubnx8ssv07dvX/r160dycjKrV6+2jaP2+uuvEx8fT0hICL17977M1sQFcltQCNHi5b/3JYYeHdCHBrJuz05OnUlDr9XRpcugBs9iNjiyq380YTvWYy0qQevmUqWNo6MjDz74IC+++CLvvvsud9xxR4PnbMkC/XzrfGDPy+3vSmzcuLHKvD+PjfbnYTwefPBBHnzwwYtu6+abb5Y3AtSCFFdCiBbtkRG3Encwl89baTn+aBybTleOwO7v5IHB4KRKptNt27H51EZGOOgu2ubhhx9m3rx5bNiwgaNHj9KlS5cGTNiy1eWraETzJLcFhRAtWr/T58j38KDk5kl4Rt/GmYJzAAQ6eagXSqMBNBR/t4HCL36utklISAhjxowBYOHChQ0YTghxOVJcCSFatBRHDQm9olC0Wg4c3IiiWAkO7oirg6Pa0Shes43sJ16nIiOn2uUXOrb/97//pbS0tCGjCSEuQYorIUSLdtBNy8nIDlitVg4d3Ahc2fAL9cV4Np2n92+hsKyM5YNvJypmOFExwxl9+1hbm2uvvZawsDAKCgr44YcfVEwrhPgzKa6EEC2SYrWS+8Ji2pgqO/emph2jsOg8jo4udOjQV+V0lWNmtbphMgeiYxhaoDD0uilEjp+LMfuPFzxrtVruvfdeoPLqlRCicZDiSgjRIpVu3EPeW5/i9vv4iEeP7gCgU8f+ODjoL7FmwzreoRPnvbwZtrHqe+EAW3H1008/kZNT/e1DUXvyguymSe3zJsWVEKJFyl/+PQ7hQZwxQEVFOceP7wGgS9eGH37hUhStlnXXXc8vw6+vdnmXLl3o06cPFRUVfPmlPMVWVy68PqakpETlJKI2Lpy3v74GqKHIUAxCiBanIiOHkjXb8Pz7bfDzt5w6dRCTqQR3dx9CQzqqHa+KPG9vnMtMeOSdR1vNv8jvu+8+9u/fzxMzZ7Hk85V2ywL9fGXogFrQ6XR4eXnZXnbs4uLS4APKiiunKAolJSVkZWXh5eWFTnfx4UzqkxRXQogWp/DLNaDV4jy0L/z8LUeObgegS+eBaDSN84K+S3ExE5d9yAetqr5896677iIuLo7iwgICb5iCm98fr4luyMEum5sLL8W+UGCJpsPLy0vVl5pLcSWEaHFcru2HtbAYrZsL5RVmTp06AKDKiOw1VebsTHpQG+48m4xirkCj/+PrOzAwEHcvHwrzzpGyay1dRz+gYtLmQ6PREBgYSOvWrTGbzWrHETWk1+tVu2J1gRRXQogWR+frhcuwfgCk5udgsVTQyrcNrVuHqpzs0vb36cttKckUrliNx/hb7Jb5tA6gMO8cybvW0OWmv8strDqk0+lU/2UtmhYproQQLcLo28dizM5lxHkLrcwKh1wrb/8dz0gDKjuyN/aC5LyPL0dcNOhfW4b72BvQOBpsy7x8W3HG4ERRVhrnko/iG9FVxaRCtGyNs3OBEELUMWN2LpH3vcCd5Z50bdWB4NjK192cL698qqhLl2iVE9bMRg8t+rAgLOcL7ObrdA4E97oGgOSda9SIJoT4nRRXQogWI/hMGj7nz3GyXXsAjh7bWTm/TQe8PP3UjFZjuXoNPk9OQuvpXmVZ2IAbAEjb+wtWS0VDRxNC/E6KKyFEi9Hj0AGKXVzJCAgE/hg4tKlctfqzwhWrKdm4x26ef+e+GFw9MRXlkX3yoErJhBBSXAkhWgZFoduvh0kOj0DRajl/PpPMzGQAOnUaoG62Wij8bDW5z75rNxK1VudAm55DADizf5Na0YRo8aS4EkK0CBogfsRIjnXqDMCJE3sB8NI74+JS9RZbY+d2+wjKj56idMNuu/nBfYYBkH5gE4q16phYQoj6J8WVEKJFUDQaMgKDyPP2AeBE4j4AWjm6qRmr1gzdI9FHhpH3zmd28/079cXByYXSvGxyk4+qlE6Ilk2KKyFEi3BfZgURSScBKCrKIz298v+banGl0WhwHT2U0i37KT+RbJuv0zsS1L1yMNT0BLk1KIQapLgSQjR7FVnnuOW8FbeiIgAST+4HFAID2+KkU+fFrnXBeVBPvB6/D4eg1nbzg3sPA+BMwka7PllCiIYhxZUQotkrid+BFUgLrhyB/cTxyv5WHTr0VTHV1dPo9bhc279K36qArgPR6Q0UZadTWlKsUjohWi7Vi6uFCxcSERGBk5MTUVFRbNmy5aJtjUYj99xzDx07dkSr1TJt2rQqbZYtW4ZGo6kylZWV1Xq/QoimrXjtNs4YKt/PV1ZWTEpqZV+kDpFNr7gynk3noUfj/pj+MZ1Pet1E51N/vFxY7+RCQJfKJyDzcuSlw0I0NFWLqy+++IJp06Yxe/ZsEhISiImJYdSoUaSmplbb3mQy4efnx+zZs+nZs+dFt+vh4YHRaLSbnJycar1fIUTTpZSbKd24h0Tnyq+7U6cOYLVaaOXbBl/fQJXTXTmLoiE4dtIf08jJhHiHcI/ZBf50C7BN72EA5OVmqxNUiBZM1eJq/vz5TJo0icmTJ9O5c2cWLFhASEgIixYtqrZ9eHg4b775Jvfffz+enp4X3a5GoyEgIMBuupr9CiGaLsVqxXvGRI44V7438MSJyqcEO3SIUjNWnTrWqQsdMdAm/YxtXpseg9FodZSVFHPixAkV0wnR8qhWXJWXl7Nv3z5iY2Pt5sfGxrJ9+/ar2nZRURFhYWEEBwczevRoEhISrnq/JpOJgoICu0kI0fhpnRxxuaYv5/QazOZyTidVjlze1Ptb/Vl6m2DOY6F3wj7bPIOrB/6dKgvIb775Rq1oQrRIDmrtOCcnB4vFgr+/v918f39/MjIyar3dTp06sWzZMrp3705BQQFvvvkmgwcP5uDBg0RGRtZ6v/PmzeO5556rdS4hRP0bfftYjNm5dvNuyq3ArNVgPJdFSfJhzOZyPDx88fcPVydkPVC0WnZRxjUHD7D6xpux6nRA5a3BjKO7WblyJU8++aS6IYVoQVTv0K7RaOw+K4pSZd6VGDhwIPfddx89e/YkJiaGL7/8kg4dOvD2229f1X5nzZpFfn6+bUpLS6t1RiFE/TBm5xI5fq5t6nzXs9x7TkPXiAFYLBbbqOwdIvte1fdMY/SLppQVd91jK6wA2vSMAWDPnj2kp6erFU2IFke14qpVq1bodLoqV4uysrKqXFW6Glqtln79+pGYmHhV+3V0dMTDw8NuEkI0bqGpyThYLJwNbINVUTh58gDQvPpbXZCnsWLWG+w6tTt7+uLiXvldtXr1arWiCdHiqFZcGQwGoqKiiI+Pt5sfHx/PoEGD6mw/iqJw4MABAgMDG3S/Qgj1tTt1ihJnZ857e1NgLqWsrAhnZzeCgzuoHa1e+GcYmf7Gq7gUF9nmeXr7AvDjjz+qFUuIFke1PlcAcXFxjB8/nr59+xIdHc37779PamoqU6ZMASpvxaWnp7N8+XLbOgcOHAAqO61nZ2dz4MABDAYDXbp0AeC5555j4MCBREZGUlBQwFtvvcWBAwd49913a7xfIUTz0PZUIsaAQNBoyC2vHEyzbUQPtFrdZdZsmgrd3fE+f44ehw6yM3owAJ4+rTCmJhEfH09ZWZndsDRCiPqhanE1btw4cnNzef755zEajXTr1o3Vq1cTFhYGVA4a+texp3r37m37/3379vHZZ58RFhZGcnIyAHl5eTz00ENkZGTg6elJ79692bx5M/3796/xfoUQzcOJjp2o0FV+zZ0zVRZX7dr1UjFR/TI5OZPeJpjufyqunF3dCAoK4uzZs2zatImRI0eqnFKI5k/V4gpg6tSpTJ06tdply5YtqzLvcu/JeuONN3jjjTeuar9CiObhYM/eeObnk1+QQ7GlHI1GQ0REd7Vj1avTEe0YtnkDnnl55Ht5odFouOmmm/jggw/44YcfpLgSogGo/rSgEELUh/CkU4QlJwGVo7IDtAmKxNnZTcVU9S8lLJwKnY7Ox47Y5t10001AZb8reZGzEPVPiishRLM0fF08Ufv2AHDqVOXAoe3aXfy1Wc2F2WBg1W13sKfvH10hhg8fjqOjI0lJSfz2228qphOiZZDiSgjR7GgtFoLPpJHlH4DZXE5KSuWLmptzf6s/K/D0xqW0xDYsg5ubG8OGDQPghx9+UDGZEC2DFFdCiGYnIMOIwWwms7U/qanHqKgox1HrgJ9fiNrRGoaicPfnnzBs43rbrNGjRwMyJIMQDUGKKyFEsxOWkoxFqyPXtxWnTh8AwMfg2uxGZb8ojQazXk/3wwdtsy70u9q6dSvnz59XK5kQLYIUV0KIZqfU2ZkTkR2o0Olsndl9HV3VDdXAksLbEpCZQZCp8tZgREQEnTt3xmKxsHbtWpXTCdG8SXElhGh2jnTtzrYh15Cbe5b8/Bx0Oj3eBhe1YzWoM8EhlOv1RBdabfPk1qAQDUOKKyFEs+JYVkpQehooiu2qVWhoJ3SalvV1Z3FwIDU0jKiiP4qrC7cGV69ejcViUSuaEM1ey/q2EUI0ex1OHOehD9/DuayUU6cvDMHQS91QKtnVfyALAv941c+gQYPw9PQkNzeXvXv3qphMiOZNiishRLMSmppCvocn57Vw5swJANq1bf7jW1Wn1MUVFwUUa+XVK71ez4gRIwBYs2aNmtGEaNakuBJCNCvBaalk+/mRknIUq9WCt3cA3t7+asdSzbA8K+mxD9k+x8bGAkindiHqkRRXQohmQ6coBBnPku3XmuSkwwDN/l2Cl5PnAKaDxzEdPQVge7fgzp07yc/PVzOaEM2WFFdCiGbD1wwlLq5k+bUmKflXANq28OLqlJMGjbsLRd+sAyAsLIyOHTtisVhYt26dyumEaJ6kuBJCNBtZBg3LJk7ihINCXl4WWq2O0NDOasdSlUWjwXlgT4pW/WJ7abPcGhSifklxJYRoNhysCo4mE0kplVet2rSJxGBwUjmV+pxjoqg4k4E5MQX449bgmjVrbAWXEKLuSHElhGg2Xkk202/PTpKkv5UdQ9f2BHz6MoYO4QAMGzYMvV5PcnIyiYmJ6oYTohmS4koI0SxYCooIKofzLq6kpBwFpL/VBRqdFq2zE5aCIhSrFVdXV4YMGQLIrUEh6oMUV0KIZsF04De0QIJSQnl5Gc7Obvj7h6kdq9GwZJ8ntf/dlG7eB9jfGhRC1C0proQQzYJp/zHKNHAoOxmA8PBuaFrYK28uRdvKC62zIwWfrwb+KK42bNhAeXm5mtGEaHbkm0cI0SyYDh7nrEFDUvLv/a3C5Zbgn2k0Gpyv60/Jj5ux5BfSo0cPWrduTXFxMdu2bVM7nhDNihRXQohmwe/1f/GZpwWjMQmAiIhuKidqfFyG9Ucxmyn6dj1arVaGZBCinkhxJYRoFpRyM6dK8gCFVq3a4O7uo3akRkfn44lj786U7ah8obX0uxKifjioHUAIIa5WyfpdnHt5CZkF5wC5JXgp3jMmYujaHoDrr78egISEBDIzM/H3b7nvYBSiLsmVKyFEk1e26zDlp89wpvA8IONbXYrW2QlLZi4VGTn4+/vTq1cvANavX69uMCGaESmuhBBNXlnCMVID3Ckxm9Dp9ISEdFQ7UqNW+MXPpA66D2tRCcOHDweQ9wwKUYekuBJCNGmKomBKOMZObSkAwcGR6PWOKqdq3Jz6d0cpLqHw67WMGDECgPj4eHkVjhB1RIorIUSTVpFixJpXyNbzZwEID+uqcqLGz6G1D079u5P/4UqGDBmCXq8nNTWVU6dOqR1NiGZBiishRJOm8/PG++VpbEs6DkCYFFc14nrjNZiPJ6M7cILo6GhAbg0KUVekuBJCNGlaV2eOGizkFRWh1+kICIhQO1KTYOgeiaFrOyoycmy3Bn/55ReVUwnRPEhxJYRo0s69tpS1K74GIMDNG61WvtZqQqPR4Dv3MZyH9LF1al+/fj1Wq1XlZEI0fTLOlRCiyVIsFvLe+ZyNSuWo7AHuXuoGamKeeuY58s7nY7BY0ep0nDt3jq5RA2kXEc4Pq75UO54QTZb8E08I0WSZT6ZSWlTE7rMpAAS4e6ucqGnJzSvg+jb9mZGpIbhDXwAc2/bHmJ2rcjIhmjYproQQTVbZ/mPsryjEVGEmsJUfHo4uakdqco536IRZrydG5wZA5m97VE4kRNMntwWFEE2WKeE3djqZIR+ujeqPJqtY7UhNjtlg4Gjnrow9sJNPgezEg5T6tiYqZniVtoF+vnK7UIgakOJKCNFkOQ/pw87PygAY1rc/m1dvUDlR03SkazfGHT6Ip5Mb+WVFmEzlRI6fW6Vd4n//rUI6IZoe1W8LLly4kIiICJycnIiKimLLli0XbWs0Grnnnnvo2LEjWq2WadOmVWnzwQcfEBMTg7e3N97e3owYMYLdu3fbtZkzZw4ajcZuCggIqOtDE0LUM1P3CA4Y0wAYFtVf5TRNl8nJmZ2DhhD8+zsZLeWlKicSomlTtbj64osvmDZtGrNnzyYhIYGYmBhGjRpFampqte1NJhN+fn7Mnj2bnj17Vttm48aN3H333WzYsIEdO3YQGhpKbGws6enpdu26du2K0Wi0TYcPH67z4xNC1B9zqpGfX1+I1WqlQ2g4wa391Y7UpJ3o0InAjn0AsJSXqZxGiKZN1eJq/vz5TJo0icmTJ9O5c2cWLFhASEgIixYtqrZ9eHg4b775Jvfffz+enp7Vtvn000+ZOnUqvXr1olOnTnzwwQdYrdYqIw87ODgQEBBgm/z8/Or8+IQQ9adk7XbWLP0UgGFR/VRO0zwMcPQFwGoup7y0SOU0QjRdqvW5Ki8vZ9++fcycOdNufmxsLNu3b6+z/ZSUlGA2m/Hx8bGbn5iYSFBQEI6OjgwYMID//Oc/tG3b9qLbMZlMmEwm2+eCgoI6yyiEuHJlCcfYoRQClf2tRPWMZ9N56NG46pdlZBL8p88uPq2J0DmTZCkl+0QCbXrGNExIIZoZ1YqrnJwcLBYL/v72l/L9/f3JyMios/3MnDmTNm3a2F7vADBgwACWL19Ohw4dyMzMZO7cuQwaNIgjR47g6+tb7XbmzZvHc889V2e5hBBXJ3XHXk6WFqDRaBjaW65cXYxF0RAcO6naZWeWvmD3udDDk67ewSTlJJL12z4proSoJdU7tGs0GrvPiqJUmVdbr7zyCp9//jmrVq3CycnJNn/UqFHccccddO/enREjRvDjjz8C8PHHH190W7NmzSI/P982paWl1UlGIcSV+9std7I58RgA3k6uPDl7Dg89GocxI1PlZE2fT9fKq4B5h+ruDoIQLY1qxVWrVq3Q6XRVrlJlZWVVuZpVG6+99hr/+c9/WLt2LT169LhkW1dXV7p3705iYuJF2zg6OuLh4WE3CSHUUZh5jnhHCwCRPYYSHDuJ4NhJWCwWlZM1fZ7dogHIyjlDWeF5ldMI0TSpVlwZDAaioqKIj4+3mx8fH8+gQYOuatuvvvoqL7zwAj///DN9+/a9bHuTycSxY8cIDAy8qv0KIRpGtkHDDktlv8ew0C4qp2leXN088dQ5ApB9IkHlNEI0TaoOIhoXF8f48ePp27cv0dHRvP/++6SmpjJlyhSg8lZceno6y5cvt61z4MABAIqKisjOzubAgQMYDAa6dKn8gn3llVd4+umn+eyzzwgPD7ddGXNzc8PNrfL1DjNmzODmm28mNDSUrKws5s6dS0FBARMmTGjAoxdC1JZPfjEFedlotTqCgzuoHafZcTM4k19qIuvYXkKirlM7jhBNjqrF1bhx48jNzeX555/HaDTSrVs3Vq9eTVhYGFA5aOhfx7zq3bu37f/37dvHZ599RlhYGMnJyUDloKTl5eXceeeddus9++yzzJkzB4AzZ85w9913k5OTg5+fHwMHDmTnzp22/QohGi9FURiSnMsvQGBgWwwGp8uuI66Mt8GF9NI8KnbE4zBuOhV6vdqRhGhSVH/9zdSpU5k6dWq1y5YtW1ZlnqIol9zehSLrUlasWFGTaEKIRsh8Ko395fmA3BKsL556ZzQaDckVxYzbs5XkQdeqHUmIJkX1pwWFEOJKlO4+zC5zZXEVGtZZ5TTNk16rw98/HABl68/qhhGiCZLiSgjRpByN30imtRydTk+boEi14zRbYaGVhevpMyfwOn9O5TRCNC1SXAkhmpTNx48A0KZNe/R6g8ppmq+wsK4A7KjIJzw5SeU0QjQtUlwJIZqUvX6VBZX0t6pfwcEd0Gp1pFvK2Bkg714V4kpIcSWEaDIspWVs3LoFgLAwKa7qk8HgRGBg5ftW8w5vR19ernIiIZoOKa6EEE3GzqdfI+fcOXRare0Xv6g/F64OOq9ZyTWbN6obRogmRIorIUSTsW7dOgBau3qi06k+kkyzd+Hq4G7TOboePqhyGiGaDimuhBBNgmKxsOX3zuwB7t4qp2kZ2rRpj06n55y5lKKMFNqYLj3OoBCikhRXQogmofTgcXaVVQ4J4O/mpW6YFsLBwUCbNu0B2GYtYmChVeVEQjQNUlwJIZqEPd//RKFiwcPVFR8XN7XjtBgX+l1tcCgnvEyKKyFqQoorIUSTsMvFAsDgnn3QauSrq6GE/j6Y6L7SXD7016mcRoimQb6hhBBNwsZ16wEY2qefyklalsDAtjg4GCgpLYTiYqylJrUjCdHoSXElhGj0So6fZsvvTwpe06evymlaFgcHPcFtKl8z1Db9HJkPPatyIiEaPymuhBCN3s7PV1FkqcDb3Z0e7TuoHafFCf19SIZ95fmUbtqLYpIBRYW4FCmuhBCN3vo1awEY3CsKrVa+thpaaEgnAH4ry8NSUkbpDhnzSohLkW8pIUSjt/nIIQCG9pZbgmoIDGyLXu9ImaWCRHcdJet2qh1JiEZNiishRKNWcjKFvYXZgPS3UotO50BwcOXt2H0+DpTt+VXlREI0brUqrpKSkuo6hxBCVCvhbAqlWPHx8KRr2/Zqx2mxLox3tdvRjP+S51VOI0TjVqviqn379lx77bV88sknlJWV1XUmIYSw2bhlCwAxvaW/lZpCQyv7XW379SAVeYUoirwKR4iLqdU31cGDB+nduzf//Oc/CQgI4OGHH2b37t11nU0I0cIpisLP73wAyC1BtQUERKDX6jhfWMCWJ14k6/9eUDuSEI1WrYqrbt26MX/+fNLT01m6dCkZGRkMGTKErl27Mn/+fLKzs+s6pxCiBfr7yDHszUgDYMNPG3jo0TgeejQOY0amyslaHq1Wh5+bJwA7zhsp2bAbxSqvwxGiOld1jd3BwYHbbruNL7/8kpdffplTp04xY8YMgoODuf/++zEajXWVUwjRAlkSUynDiouzO11veZTg2EkEx07CYrGoHa1FCvj9hdk7CrOxnsun/OhpdQMJ0UhdVXG1d+9epk6dSmBgIPPnz2fGjBmcOnWK9evXk56ezpgxY+oqpxCiBSrNOw9Uvt9Oo9GonEb4u3sDsCPpOBa9A6Vb9qqcSIjGqVbF1fz58+nevTuDBg3i7NmzLF++nJSUFObOnUtERASDBw/mvffeY//+/XWdVwjRQihWKynF+QCEhnVWOY0A8HZ2w9PNjYLiYk4Ee1C6Rb7jhahOrYqrRYsWcc8995Camsq3337L6NGjqzzFExoaypIlS+okpBCi5SkrKSGhogD4YxgAoS6tRsPgnn0AONDJn1av/0vlREI0TrUqruLj43nyyScJCAiwm68oCqmpqQAYDAYmTJhw9QmFEC3Srr17sSgKrq6e+PgEqh1H/G7o709tbkk8CuYKldMI0Tg51Galdu3aYTQaad26td38c+fOERERIZ1NhRBXbfXc+YD0t2pMjGfTObe2EID1u3fy5TVj+c1Vx2ofHYF+vvyw6kuVEwrRONTqytXFBo8rKirCycnpqgIJIYS1uJSNWzYDEBYq/a0aC4uiofuYx3BycqXCaiHP0YUYtwgix8/FmJ2rdjwhGo0runIVFxcHgEaj4ZlnnsHFxcW2zGKxsGvXLnr16lWnAYUQLU/uhl0cKK/sbxUq/a0aFY1GS0hIJxIT97FFU8rw1GR0FXJ7UIg/u6LiKiEhAai8cnX48GEMBoNtmcFgoGfPnsyYMaNuEwohWpwtn3+FGQUXvQFvb3+144i/CAvtTGLiPhKKMtFXtCbobDq/qR1KiEbkioqrDRs2APD3v/+dN998Ew8Pj3oJJYRo2TZs3gSAv5u39LdqhELDKq8mJmUlU+wbSESSDCYqxJ/Vqs/V0qVLpbASQtQLRVHYbTAD4O/upW4YUS2/Vm1wdnbHbC5nac8uJPTqrXYkIRqVGl+5uv3221m2bBkeHh7cfvvtl2y7atWqqw4mhGgZRt8+1q4ztMVSwaGkRAC0pdKXpzHSaLSEhnbi+PE97C/JJsLgqHYkIRqVGhdXnp6etsvznp6e9RZICNGyGLNziRw/1/bZ9ZuPOahsxsPDF/3VvaFL1KPQ0M4cP76HtOQjPP79N+SVyUuchbigxsXV0qVLq/1/IYSoKxqrFc22NcDv41tlZamcSFzMhVHz04ynaF/uR08f6RsnxAW1+mdhaWkpJSUlts8pKSksWLCAtWvX1lkwIUTL0yb9DHtLK28RyitvGjdf3yBcXT2pqChnk5sDXUrkypUQF9SquBozZgzLly8HIC8vj/79+/P6668zZswYFi1adEXbWrhwIRERETg5OREVFcWWLVsu2tZoNHLPPffQsWNHtFot06ZNq7bdypUr6dKlC46OjnTp0oVvvvnmqvYrhGgYIUcP8WtFEVB55Uo0XhqNhtCQTgBsUUroVKqgWKXAEgJqWVzt37+fmJgYAL7++msCAgJISUlh+fLlvPXWWzXezhdffMG0adOYPXs2CQkJxMTEMGrUKNv7Cf/KZDLh5+fH7Nmz6dmzZ7VtduzYwbhx4xg/fjwHDx5k/PjxjB07ll27dtV6v0KIhlFyYDsWFDw9/fD0bKV2HHEZF4ZkSCjOws0K5ceT1Q0kRCNRq+KqpKQEd3d3ANauXcvtt9+OVqtl4MCBpKSk1Hg78+fPZ9KkSUyePJnOnTuzYMECQkJCLnr1Kzw8nDfffJP777//op3qFyxYwPXXX8+sWbPo1KkTs2bNYvjw4SxYsKDW+xVCNIwNDiZAXnnTVISGVJ6npJxUvvYCnY887CQE1LK4at++Pd9++y1paWmsWbOG2NhYALKysmo8/lV5eTn79u2zrXtBbGws27dvr00soPLK1V+3OXLkSNs2a7tfk8lEQUGB3SSEqFsHi7OBP66IiMbNxycANzcvLJYK1moKcfD3VTuSEI1CrYqrZ555hhkzZhAeHs6AAQOIjo4GKq9i9e5ds8HkcnJysFgs+Pvbv9rC39+fjIyM2sQCICMj45LbrO1+582bh6enp20KCQmpdUYhRFXhB/aSffYUIFeumgqNRmPrG1ecd55zr3+sciIhGodaFVd33nknqamp7N27l59//tk2f/jw4bzxxhtXtK2/vtpCUZSrft1FTbZ5pfudNWsW+fn5tiktLe2qMgoh/kRRCFi1HEVR8PYOwN3dR+1EooYuPNWZUZTH+Zc+xHwmU+VEQqjvit4t+GcBAQEEBATYzevfv3+N12/VqhU6na7K1aKsrKwqV5WuNNeltlnb/To6OuLoKKMQC1Ef/LKzOJR/FpCrVk1N2O+3cNPKCilxsVC26xD64OtVTiWEump15aq4uJinn36aQYMG0b59e9q2bWs31YTBYCAqKor4+Hi7+fHx8QwaNKg2sQCIjo6uss21a9fatllf+xVC1F5k4nF2VOQDf/yyFk2Dp6cfHh6tsCoKB7x0lO08qHYkIVRXqytXkydPZtOmTYwfP57AwMBa38aLi4tj/Pjx9O3bl+joaN5//31SU1OZMmUKUHkrLj093TamFsCBAwcAKCoqIjs7mwMHDmAwGOjSpfIL+fHHH+eaa67h5ZdfZsyYMXz33Xf88ssvbN26tcb7FUI0LP8jh/itohiQ8a2aGo1GQ1hoZw7/uoWV2ckEf/YdM3b+ZFse6OfLD6u+VDGhEA2vVsXVTz/9xI8//sjgwYOvaufjxo0jNzeX559/HqPRSLdu3Vi9ejVhYWFA5aChfx176s8d5vft28dnn31GWFgYycnJAAwaNIgVK1bw73//m6effpp27drxxRdfMGDAgBrvVwjRsLZqKt/40KpVG1xd5XH+piYsrAuHf93CAT2c6TOIDjfdgqKtvDGS+N9/q5xOiIZXq+LK29sbH5+66XA6depUpk6dWu2yZcuWVZmnKMplt3nnnXdy55131nq/QoiGtUFXDsgtwaYq9PdO7ann0tnUu5etsBKiparVT8ALL7zAM888Y/d+QSGEqI0OJVYyExMAeZ9gU+Xh4YOzTo+iKJj2byUkteaDSQvRHNXqytXrr7/OqVOn8Pf3Jzw8HL1eb7d8//79dRJOCNH83ZlewopzRkAj/a2aMC+9C6WWfEr2buAGYwEfPCx3BkTLVavi6tZbb63jGEKIlqjCmE1qcR4A/v5hODm5qhtI1Jq3wQVjWT57S3MITk9DV1GBxaHWo/0I0aTV6m/+s88+W9c5hBAtUMnGPWw3yxAMzYGXwRmA1IJsCh3KCDqbTlqoPCQkWqZa9zrMy8vjww8/ZNasWZw7dw6ovB2Ynp5eZ+GEEM1bycY9bL8wvpXcEmzSDFoHWrVqA8B2axFhKcnqBhJCRbW6cnXo0CFGjBiBp6cnycnJPPjgg/j4+PDNN9+QkpJiNy6VEEJcTLqljLOWMjQaLcHBHdWOI65SaGgXcnLSiXe0MkKeGBQtWK3+9sfFxTFx4kQSExNxcnKyzR81ahSbN2+us3BCiOYtoXPlK6eCAtvi6OischpxtS7c2t1Rkc++vv1UTiOEempVXO3Zs4eHH364yvw2bdpUeWefEEJUp/xUKht++QWQ/lbNRWhIJ0BDbu5ZHJMTcSwrUzuSEKqoVXHl5OREQUFBlfnHjx/Hz8/vqkMJIZq/rOmvsH7DRuCPQShF0+bs7Ia/fygAXT6YT7dfD6ucSAh11Kq4GjNmDM8//zxmsxmofLdUamoqM2fO5I477qjTgEKI5sdaVMJvO/eQYSpGq9HQpk2k2pFEHblQKG/QlBKamqxuGCFUUqvi6rXXXiM7O5vWrVtTWlrK0KFDad++Pe7u7rz44ot1nVEI0cyUbk9gZ0kuAH6unuj1BpUTiboS/vst3l2m8/LEoGixavW0oIeHB1u3bmXDhg3s27cPq9VKnz59GDFiRF3nE0I0Q6Ub97JDVwqAv5uXumFEnQoJ6YRWqyPLVEhpZhpu3u5qRxKiwV1xcWW1Wlm2bBmrVq0iOTkZjUZDREQEAQEBKIqCRqOpj5xCiGakoqiIHabzAAS6e6ucRtQlg8GJoMB2nEk/wWZrIYHlbmpHEqLBXdFtQUVRuOWWW5g8eTLp6el0796drl27kpKSwsSJE7ntttvqK6cQohlJuzma86ZS3Jxd8HWVKxvNzYWnPz9v40Ois4x3JVqeK7pytWzZMjZv3sy6deu49tpr7ZatX7+eW2+9leXLl3P//ffXaUghRNM3+vaxGLNzca9QyD6TAoCn3onMzGxCVc4m6lZ4eDe2bf+WtORf6erZR+04QjS4K/onxeeff85TTz1VpbACuO6665g5cyaffvppnYUTQjQfxuxcIsfP5THnLrjllQDQqe8oLBaLyslEXQsKaodeb6CkpJAnjheglJvVjiREg7qi4urQoUPccMMNF10+atQoDh48eNWhhBDNk8ZqJfTkcQ6W5AAQFt5V5USiPuh0DoQEdwIgwZSH6dAJlRMJ0bCuqLg6d+4c/v7+F13u7+/P+fPnrzqUEKJ5CjSe5URBJiZrBS4uHvi1ClY7kqgnF/pdbTXnUbZbBhMVLcsVFVcWiwUHh4t309LpdFRUVFx1KCFE89T+ZCJbKyrf7hAe1lWeLm7GLlyV3GMuoGBHgspphGhYV9ShXVEUJk6ciKOjY7XLTSZTnYQSQjRPvrk5bKYYkPcJNnf+rUNxdnajtLSI3Vu3ESJD9YgW5IqKqwkTJly2jTwpKIS4mO+HDeXo2jcB6W/V3Gk0WkJDO3P8+B4O39yfO6WwEi3IFRVXS5cura8cQohmTm9VOH90L4pixcurNV6e8pL35i48vBvHj+9hw45tPKd2GCEakIzuJoRoEPdkW3Bb/QVQ2d9KNH8XzvPO/XtJfeYtldMI0XCkuBJCNIiexVZ2l/4+BIMUVy2Cl1drXPWOmK1WNq38Tu04QjQYKa6EEPWuIj0Tx7JyUkoqh2qRzuwtg0ajIeD3d0duTjqOJa9Q5URCNAwproQQ9a5k4162l+cB0Lp1GC4u8j7BluJCcbWtPI+yPb+qnEaIhiHFlRCi3pXtO0K8JQ+AcLlq1aIE/l5cHbMUk7phu8pphGgYUlwJIeqdz7P/x5aKfKDyCTLRcpzPzsbb2Q2AcV8sISpmOFExwxl9+1iVkwlRf6S4EkLUK0VROLo3gWKzCZ1OT0hIR7UjiQZkUTR06DEUgBLfECLHzyVy/FyM2bkqJxOi/khxJYSoV+fnf8w3j8wEICS4A3p99W94EM1XxO9XK88d2kZr41mV0whR/6S4EkLUq5JfdrIlr/IXakREd5XTCDUEB3fAwUHPeVMxbvu2qR1HiHonxZUQot5YzhdQsO8IO84ZAQiPkP5WLZGDg4GQ4E4AZB3ZqXIaIeqfFFdCiHpTumkvCaY8SszlODnoae0XonYkoZILhfXxs4mgKCqnEaJ+SXElhKg3JZv2sN2lAoBAdx80GvnKaaku9LvaV3YOr0yjymmEqF/yTSeEqDe+T09hh4sFgEAPb5XTCDX5+YXg6uJBKVZSjafUjiNEvVK9uFq4cCERERE4OTkRFRXFli1bLtl+06ZNREVF4eTkRNu2bVm8eLHd8mHDhqHRaKpMN910k63NnDlzqiwPCAiol+MToiXLTk/nQNJJ4I+RukXLpNFoCP/9gYbk5CMqpxGifqlaXH3xxRdMmzaN2bNnk5CQQExMDKNGjSI1NbXa9klJSdx4443ExMSQkJDAU089xWOPPcbKlSttbVatWoXRaLRNv/76Kzqdjr/97W922+ratatdu8OHD9frsQrR0uQt/oJvJs9AURS6tWuPiwzB0OJduDVYtHudykmEqF8Oau58/vz5TJo0icmTJwOwYMEC1qxZw6JFi5g3b16V9osXLyY0NJQFCxYA0LlzZ/bu3ctrr73GHXfcAYCPj4/dOitWrMDFxaVKceXg4CBXq4SoR8X/28Sms0kADO8XTe7xNJUTCbVdGJ3/zLl0QkvD1Q0jRD1S7cpVeXk5+/btIzY21m5+bGws27dX//6pHTt2VGk/cuRI9u7di9lsrnadJUuWcNddd+Hq6mo3PzExkaCgICIiIrjrrrs4ffr0JfOaTCYKCgrsJiFE9Sx5hZTu+ZUtBRkADO8/UOVEojFwc/PC37cNCuCSfV7tOELUG9WKq5ycHCwWC/7+/nbz/f39ycjIqHadjIyMattXVFSQk5NTpf3u3bv59ddfbVfGLhgwYADLly9nzZo1fPDBB2RkZDBo0CBycy/+OoZ58+bh6elpm0JC5JFyIS6mdMNuTpmLOVuQh6PBwOCevdWOJBqJ0LY9ACjMk9ffiOZL9Q7tGo3G7rOiKFXmXa59dfOh8qpVt27d6N+/v938UaNGcccdd9C9e3dGjBjBjz/+CMDHH3980f3OmjWL/Px825SWJrc4hLiYknU72eFuBWBIzz44OzqpnEg0Fm1/79SeWHTe9v0tRHOjWnHVqlUrdDpdlatUWVlZVa5OXRAQEFBtewcHB3x9fe3ml5SUsGLFiipXrarj6upK9+7dSUxMvGgbR0dHPDw87CYhRPW8n3iAHT6VXTqv6zdA5TSiMQkJ6YhBpyfXWs6hQ4fUjiNEvVCtuDIYDERFRREfH283Pz4+nkGDBlW7TnR0dJX2a9eupW/fvuj1erv5X375JSaTifvuu++yWUwmE8eOHSMwMPAKj0IIUZ1SUxmbj1U+gRs7cLDKaURj4uBgICS8KwA///yzymmEqB+q3haMi4vjww8/5KOPPuLYsWNMnz6d1NRUpkyZAlTeirv//vtt7adMmUJKSgpxcXEcO3aMjz76iCVLljBjxowq216yZAm33nprlStaADNmzGDTpk0kJSWxa9cu7rzzTgoKCpgwYUL9HawQLcSrA27iuZibKSs34aJ3ZMH8d3no0TiMGZlqRxONRNuIyn5Xq79aeZmWQjRNqg7FMG7cOHJzc3n++ecxGo1069aN1atXExYWBoDRaLQb8yoiIoLVq1czffp03n33XYKCgnjrrbdswzBccOLECbZu3cratWur3e+ZM2e4++67ycnJwc/Pj4EDB7Jz507bfoUQtdcrvYB3qexvFdklmpCRkwA4s/QFNWOJRqTt753at+/fR0FBgXSzEM2OqsUVwNSpU5k6dWq1y5YtW1Zl3tChQ9m/f/8lt9mhQ4dLdpRcsWLFFWUUQtRMhTGbtibYUVZ5lapt254qJxKNkbe3P356Z7LNpcSv/ok77hqndiQh6pTqTwsKIZqPkl92kGQpJavoHFqtjvCwrmpHEo1UG/fKAZ9Xf/aFykmEqHtSXAkh6kzxmm18a60cHDI4uAOOjs4qJxKNlY9X5bsm12zeJEMyiGZHiishRJ3xnvF3frLkAX/0qxGiOq3dvXHSOZCef46jR4+qHUeIOiXFlRCizpQbdKQU5wHS30pcmoNWx5CofoAMySCaHymuhBB14vwby/npudexKFbc3X3waxWsdiTRyI38fQy01d/9T+UkQtQt1Z8WFEI0fYqikL9kFfHWs0DlLcFLvcZKCIDrB1QOGL11+zaKiopwc3NTOZEQdUOuXAkhrlr5oRNYMnPZmFv5zk25JShqIjI0jFAXD8otFWzYsEHtOELUGSmuhBBXrfjnraQ4wqmsDDRoZAgGUSMajYbhnX8frf17uTUomg8proQQV634p61sb1XZy6C1m6cMwSBqbNTw6wH44bvvZUgG0WxIcSWEuGreMyexWSkEIMjDR+U0oim5LnYEThodZ7IzOXTokNpxhKgTUlwJIa6aqZUnm387DEAbj6ovSxfiYlycnLkuurJj+//+J7cGRfMgxZUQolZG3z6WqJjhvNFhKI/dehem8nLcDE6U5BWqHU00MaMGXwPAD1JciWZCiishRK0Ys3Pp9rfZ3JQPaVodAJ26D8VqtaqcTDQ1N/SqHEx09549ZGZmqpxGiKsn41wJIWqtw4njYLGwPycJgPbte5ORlqRyKtEUGM+m89CjcbbPHfVuHDcX0X/IMLp3784Pq75UMZ0QV0eKKyFErXU+dpTNrjqKc4twdHQhJKQjGWqHEk2CRdEQHDvJ9rniXBHHU/ZicW2NMTtXxWRCXD25LSiEqBWdotDx+DF+1JYA0DaiOzqd/HtN1E5Y5/4AZB7dhdVqUTmNEFdHiishRK39PPJGtuenA9A+so/KaURT5tA5Cn+tgQqzicK8PLXjCHFVpLgSQtSKRaPhN2c9WeeNaDRa2skrb8RVsBgMBHWrHJIh/1yOymmEuDpSXAkhrpiiKEwxmsnZux6A4OAOODm5qpxKNHXtfr/6mX8uR0ZrF02aFFdCiCtWfjiR6/IVjqZUDhwa2V5uCYqr19kvHCeNFnO5iYMHD6odR4hak+JKCHHFin/eSiYVnMxKBiqHYBDiapk9vBjgVDnC/w8//KByGiFqT4orIcQVK169hVVKHlarBV+fIHx8AtSOJJoDjYbuQZ0A+O6771QOI0TtSXElhLgi5lQj5UdOsq78HADt2/dSN5BoVtp0i0YD7N27l7S0NLXjCFErUlwJIa6I1tMNl8fv5WjJ78WVDMEg6lBxu070cfAA4Ntvv1U3jBC1JMWVEOKKaN1c2ONqpdxSgaurJ22CItWOJJqRCr0eJz8/AFatWqVyGiFqR4orIUSNWfIKyZ72Mt/+vBqAyMgotFr5GhF1y8+7FQCbN28mOztb5TRCXDn5VhRC1FjJLzvI+3w1P+zaDkDHDn1VTiSaI1+9E91cvbFarXz//fdqxxHiiklxJYSoseLVWzgY4Ex2/nkMOgdCQzurHUk0Qyathhs82gBya1A0TVJcCSFqRDGVU7J+F2v1lS9qDvb0lRc1i3pzyzXXAvDLL7+Qn5+vchohrowUV0KIGinZsh9rUQk/pZ4AINTLT+VEojnrccN1tNU5U15ezurVq9WOI8QVkeJKCFEjho7hnL55AOnncnBzdiHQ3VvtSKIZ07cLYaSn3BoUTZMUV0KIGtH5eLKmPBeAGwYNQafVqZxINGcarZZxMx4D4KeffqK0tFTlRELUnBRXQojLMh05Se5/PuC7TesAuHXocJUTiZagX8xgQoLaUFxcTHx8vNpxhKgxKa6EEJdV9M069nz8JafSz+BkcCR24GC1I4lmzHg2nYcejePhx/5Jj0IFgL8/+DCjbx+rcjIhakYe9RFCXFbxT1tY52mBdBgxIBo3Fxe1I4lmzKJoCI6dBECPss/48dhZCouKSc+UAUVF06D6lauFCxcSERGBk5MTUVFRbNmy5ZLtN23aRFRUFE5OTrRt25bFixfbLV+2bBkajabKVFZWdlX7FaIlGn37WG4acB3mEyl8cvIQAOdSM3jo0TiMGZkqpxMtgUv3gfhrDZhLCik4f07tOELUiKrF1RdffMG0adOYPXs2CQkJxMTEMGrUKFJTU6ttn5SUxI033khMTAwJCQk89dRTPPbYY6xcudKunYeHB0aj0W5ycnKq9X6FaKmM2bmM6hDLUaWMrPISdDoH+t86jeDYSVgsFrXjiRbAGBLKSOfWAJzPkYJeNA2qFlfz589n0qRJTJ48mc6dO7NgwQJCQkJYtGhRte0XL15MaGgoCxYsoHPnzkyePJkHHniA1157za6dRqMhICDAbrqa/QrRkqWEhfG+jwGAtm174OTkqnIi0ZJYHByICu8JQH5uDiUlJSonEuLyVCuuysvL2bdvH7GxsXbzY2Nj2b59e7Xr7Nixo0r7kSNHsnfvXsxms21eUVERYWFhBAcHM3r0aBISEq5qv0K0ZLnevmzNPglAl87RKqcRLVH+0Bvx8PbHarXwww8/qB1HiMtSrbjKycnBYrHg7+9vN9/f35+MjIxq18nIyKi2fUVFBTk5OQB06tSJZcuW8f333/P555/j5OTE4MGDSUxMrPV+AUwmEwUFBXaTEM1dzyIrrX/6mry8LPR6R9q37612JNEClbh70LHrIABWrFihchohLk/1Du0ajcbus6IoVeZdrv2f5w8cOJD77ruPnj17EhMTw5dffkmHDh14++23r2q/8+bNw9PT0zaFhIRc/uCEaOJGnrdwOmEDAJGRfdDrHVVOJFqqW3SVbwRYvXq1vGtQNHqqFVetWrVCp9NVuVqUlZVV5arSBQEBAdW2d3BwwNfXt9p1tFot/fr1s125qs1+AWbNmkV+fr5tSktLu+wxCtGUWYtL6VpsJb7YCMgtQaEun4Bw2umcMZlMfPfdd2rHEeKSVCuuDAYDUVFRVUbdjY+PZ9CgQdWuEx0dXaX92rVr6du3L3q9vtp1FEXhwIEDBAYG1nq/AI6Ojnh4eNhNQjRnJet3caA8nzxTMU5OrkREdFc7kmjB0kNCucGp8mXhcmtQNHaq3haMi4vjww8/5KOPPuLYsWNMnz6d1NRUpkyZAlReLbr//vtt7adMmUJKSgpxcXEcO3aMjz76iCVLljBjxgxbm+eee441a9Zw+vRpDhw4wKRJkzhw4IBtmzXZrxACildv5ktz5aCNHTv2Q6eTMYeFeqw6HZGelcVVfHy8rZ+tEI2Rqt+W48aNIzc3l+effx6j0Ui3bt1YvXo1YWFhABiNRruxpyIiIli9ejXTp0/n3XffJSgoiLfeeos77rjD1iYvL4+HHnqIjIwMPD096d27N5s3b6Z///413q8QAhyuieKX9ytf1Cy3BEVjcM7Tla6ZrhypKGblypU8/PDDakcSolqq/1N06tSpTJ06tdply5YtqzJv6NCh7N+//6Lbe+ONN3jjjTeuar9CCNhcnE2ptQI3Ny9CQjqpHUcIkhw13DXhfp7+aBGff/65FFei0VL9aUEhRONT+MXPfPr+hwB06jQArVa+KoT6FI2GsTeOBmDz5s2kpKSonEiI6sk3phDCjmK1kjLnbVYn7AbklqBoXIIcXRnk5oeiKPz3v/9VO44Q1ZLiSghhx5RwjP+dOUFphRkPR2cCA9uqHUkIG62XO3f6hgOVXUcujHUoRGMixZUQwk7xD5tYWVHZkb2db+AlB9cVoqFpNBpuvelmXDU6Tp06xbZt29SOJEQVUlwJIWwUReHwl/9jX9l5tFotET4XH1hXCLW0un4QowytgOoffBJCbVJcCSEYfftYomKGMyBmOM9lHAEgwM2L/Nw8dYMJUQ0HPx/GdYkC4Msvv6SkpETlRELYk+JKCIExO5fI8XMJv+959pqLAeh/7T1YLBaVkwlRvZFzn6RtWDiFhYV88803ascRwo4UV0IIm4DP36eo8BxOTm60b99H7ThCXJSDpzv33nQLILcGReMjxZUQAgC/rExO7/wJgC5donFwqP59nUI0FreUOgGwbt06u7d5CKE2Ka6EEABE7N9NfPk5AHp0v0blNEJcXuTg/gzUe8qYV6LRkeJKCAHA2R2rKceKn18I/v7ynk3R+Ok7RvC3wA6AjHklGhfV3y0ohFBfsMnK2pxTAHTvHiNjW4lGyXg2nYcejbObF6Uz4KrRcfLkSTZs2MB1112nUjoh/iDFlRCCzNIiDlcUodXq6NplkNpxhKiWRdEQHDvJbl5+aSmjPzjNF6VGFi1aJMWVaBTktqAQgtNZ6QB07NgPV1dPldMIUXNlzs6UhLUB4Ntvv8VoNKqcSAgproRo8bL2HCQvOxOAPr1HqJxGiCvn6ezGoD5RVFRU8OGHH6odRwi5LShES/fhMy9iVqz4tQomOLiD2nGEuGLGs+lca9KwHXhh7ot8s2Y9Go2WQD9fflj1pdrxRAskV66EaMEsFRV8uL5ybKs+fUZIR3bRJFkUDRGDbsZb44C53IRrjxuIHD8XY3au2tFECyXFlRAt2E9vv09SeREGrY4u0pFdNGEpHbtwu0sQACc3yetwhLqkuBKiBVv0zrsAhPv44+jorHIaIWrPbDAwoPMgNEDG0V0UZZ9RO5JowaS4EqKFOnPmDD8n/wZAh1ZtVE4jxNXL6TuYvh6VV69Obf5O5TSiJZPiSogW6v3338dqtRLTKwovZ1e14whx1Qo8vQi5fhwAp7f9gNViUTmRaKmkuBKiBSovL+e9N94E4OHbx6qcRoi60z6iJ95u3pQX53MuO0PtOKKFkuJKiBbov28vJKuogAB3T26+ZpjacYSoM1qtlgkuwQBkpqdhtVpVTiRaIimuhGhhrFYrr77yCgCP3HUfege9yomEqEMaDW2jb8JDo8NUWsIPP/ygdiLRAklxJUQLs/r7/3E8y4ib3sDkO+SWoGh+jB06c7tnOACvvfaaumFEiyTFlRAtzEv/fgaAv8eOxtPNXeU0QtQ9Raul28Cb0KNhy5Yt7Nq1S+1IooWR4kqIFmTXrl1sO3IIvU7Ho5MeVDuOEPUmt3sfenm0BuD1119XOY1oaaS4EqIFefXVVwEYF3sjwa39VU4jRP1RtDr8g0IAWLlyJadPn1Y5kWhJpLgSooU4efIkq1auAuDxu8ernEaI+ufl7MZ1EZ2wWq0sWLBA7TiiBZHiSogW4tW5L6KgMCK8I13btlc7jhAN4h/XxAKw5IMPycnJUTmNaCmkuBKiBcjMzGT5p58C8M+p/1A5jRANJ/bv99Hd2ZuSslJ5clA0GCmuhGgB/vP885RVmOnj14ZrogepHUeIBqN1cGDWXfcD8M5bb5GVlaVyItESSHElRDN35swZ3vvgQwCe/r9H0Wg0KicSomHd8vfx9HTzpbi01PZQhxD1SYorIZq5//znP5jM5UR36U7s9derHUeIBqfVannmqdkAvPvuu2RmZqqcSDR3DmoHEELUn5SUFD78/arVnP97jKeeeY7cvIIq7YwZmQQ3dDgh6pnxbDoPPRoHgKIotHJxJ6ekkN69+9Fn4EB+WPWlyglFcyXFlRDN2PNPP4O5wkxMcDtiekfx348+JTh2UpV2Z5a+oEI6IeqXRdHY/X2/MWQ3y//3NjmZRlLTz6qYTDR3qt8WXLhwIRERETg5OREVFcWWLVsu2X7Tpk1ERUXh5ORE27ZtWbx4sd3yDz74gJiYGLy9vfH29mbEiBHs3r3brs2cOXPQaDR2U0BAQJ0fmxBqOnnyJB9/+gkAzz4ep3IaIdQX2LkfHTwDMFsryE9JUTuOaMZULa6++OILpk2bxuzZs0lISCAmJoZRo0aRmppabfukpCRuvPFGYmJiSEhI4KmnnuKxxx5j5cqVtjYbN27k7rvvZsOGDezYsYPQ0FBiY2NJT0+321bXrl0xGo226fDhw/V6rEI0tDn/monFauW60EgGRUerHUcI1Wk0GvqOuBcAY2Y6aWlpKicSzZWqxdX8+fOZNGkSkydPpnPnzixYsICQkBAWLVpUbfvFixcTGhrKggUL6Ny5M5MnT+aBBx6wG7vk008/ZerUqfTq1YtOnTrxwQcfYLVaWbdund22HBwcCAgIsE1+fn71eqxCNKRff/2Vz7+rHI19zsynVE4jROMR0q4nkX5hmFF4YtLDascRzZRqxVV5eTn79u0jNjbWbn5sbCzbt2+vdp0dO3ZUaT9y5Ej27t2L2Wyudp2SkhLMZjM+Pj528xMTEwkKCiIiIoK77rrrsu+dMplMFBQU2E1CNEaKohAXF4dVURjdoy99e/RUO5IQjYZGo2HQDX8HYEX8T1W6jQhRF1Tr0J6Tk4PFYsHf3/7lsf7+/mRkZFS7TkZGRrXtKyoqyMnJITAwsMo6M2fOpE2bNowYMcI2b8CAASxfvpwOHTqQmZnJ3LlzGTRoEEeOHMHX17fafc+bN4/nnnvuSg9TiAY3IHoIe3ZtR6vRoKvQ2Z6WAnkqUAiAwKB2tPXx5/S5TKb941G27dop47+JOqV6h/a//oVWFOWSf8mra1/dfIBXXnmFzz//nFWrVuHk5GSbP2rUKO644w66d+/OiBEj+PHHHwH4+OOPL7rfWbNmkZ+fb5vkXr1ojEwmE8n79wPQf8BNdL75HwTHTrJNFotF5YRCNA69AtviYnBkx57dfLbgHbXjiGZGteKqVatW6HS6KlepsrKyqlyduiAgIKDa9g4ODlWuOL322mv85z//Ye3atfTo0eOSWVxdXenevTuJiYkXbePo6IiHh4fdJERjMz/uSbLNZXg6uhI98Ba14wjRaLkYHIm7p/K1ODNnz6a0pETlRKI5Ua24MhgMREVFER8fbzc/Pj6eQYOqf/dZdHR0lfZr166lb9++6PV627xXX32VF154gZ9//pm+ffteNovJZOLYsWPV3lYUoqkwnk5i3uJ3ARh83d04OjqrnEiIxm3afRMJ8vbhTGkhL02conYc0YyoOohoXFwc48ePp2/fvkRHR/P++++TmprKlCmVf8lnzZpFeno6y5cvB2DKlCm88847xMXF8eCDD7Jjxw6WLFnC559/btvmK6+8wtNPP81nn31GeHi47UqXm5sbbm5uAMyYMYObb76Z0NBQsrKymDt3LgUFBUyYMKGB/wSEqL3Rt4/FmJ1r++x68CiF1gq8HZzo3j1GxWRCNH7Gs+lM+9dswj1ac/b8OV77+jPW9zmFZ3gbGbldXDVVi6tx48aRm5vL888/j9FopFu3bqxevZqwsDAAjEaj3ZhXERERrF69munTp/Puu+8SFBTEW2+9xR133GFrs3DhQsrLy7nzzjvt9vXss88yZ84coPJFtnfffTc5OTn4+fkxcOBAdu7caduvEE2BMTuXyPFzATifdJT4rZMBCHfzQ6NRvTulEI3ahdHb2yhWUpY/R3rGadIqNJT86R8sQtSW6q+/mTp1KlOnTq122bJly6rMGzp0KPt/77BbneTk5Mvuc8WKFTWNJ0SjZy03sefjF1GALl2i8cyRXw5C1JRGoyV21AN8/PGzpBzehq5TN7UjiWZA/nkrRBOmLy/Hbe6jnDcm4ezszojh96kdSYgmx791GAMG3ARA/okT5J6WV+OIqyPFlRBNlaLQ69MP+CTzCADXjxiPi4s8xSpEbQweNAZfL39yreU8ftPtascRTZwUV0I0UdfmWfjv3u8wo9C+fW86dx6odiQhmiwHBwMjb6zst/jpb/v5ad4CdQOJJk2KKyGaoLJ9R9AlpXKwoghHgzMjYyfKCNNCXKXQkE5E+lYOyfN/z86mKO2syolEUyXFlRBN0KmiPBaUVj5Je9119+Du7nOZNYQQNdG7TTsCfVqRYi5hxqyZascRTZQUV0I0IUq5mcLTqdzz0CTKFSthYV3p0WOo2rGEaDZyMzPp7B0EwHuf/pe2nbsTFTOc0bePVTmZaEqkuBKiiVAUhewn5zO13zAOnTiOo4Oe0Tc9LLcDhahDFkVD/zv/ZXt6MDvxOJ0Gj7cbsFeIy5HiSogmouCjb/hiyTI+OZcEwOCwTri7e6ucSojm6ZqYO2kT0JYii5mD7/wLjVVeei5qToorIZqAki372PfkS8wuqyysZtz3d4I8fC+zlhCitnQ6B24e8whOeieOFOfgfjxJ7UiiCZHiSohGzlpqIu3BZ5lWnkSh2UR09148M/n/1I4lRLPn5dWakaMmAbApN5Xv3likciLRVEhxJUQjd+td93JH5l4OF+Zg0DkQYHVi6vQnMGZkqh1NiGavc+eB9OoxDAW4/9//4siRI2pHEk2AFFdCNFLWMhPn3/mMpD37OJKXiUaj5dbbp9Nx9CMEx07CYpE+IEI0hOtjJ9DazZOCkmJGjx5NZkaG2pFEIyfFlRCNkGK1kvWPF/n46Rf51ZgMwPXXj6dt2x7qBhOiBdLpHLgmoitt2wSTnJzMLQNjKCsrUzuWaMSkuBKikVEUhdxn3mHTyu94svAEAP37jaJP7xEqJxOi5XJyMLDylTfxdHRid8pJJt54C4qiqB1LNFJSXAnRyJx/dSkHFi5nqukU5ZYKQjxbce21d6kdS4gWr2NYBJ++NB+dRsMXG+L514NTpMAS1ZLiSohGRFEUju9N4H5zIudKi4nq3JXB4Z3RaORHVQg1Gc+m89CjcaxY/iUD20QC8PqS9wkLiZDR20UVDmoHEEJUMielc/JMGndu/BJjUQGdw9uy8pU3+fczc9WOJkSLZ1E0BMdWDssQDHht+54ft35FWnoKFfvkHz/CnvyNEEJliqKwsM8oNvQdQ//hwzibnYWnkwtd3QL49zNzZcgFIRqh7oNv4dpr7wbAmJrEvBf/o3Ii0ZjIlSshVKSYK8h+cj4dk7MZW3qcIrOJVr5tuPvuWbi6egJwZukLKqcUQlRnQP8b0ZaVsm7Htzz179mYTCaefW6OvO9TyJUrIdRiySvEOO6fbFj2ObfkH+RcWRG+vkF2hZUQonHrd80dXNcqDIDnXnieB/7+d8xms8qphNqkuBJCJdbCYr4+sIv7C3+lxFpBQEAE99z9lBRWQjQxQSERvHbH/WiBZR9/zI03jKKgoEDtWEJFUlwJ0YAURaHgkx8wnUjm+Ree5/GkXZRXVA63cO89s6WwEqKJmjp9Gp8++E+ctTp+Wb+OmJgY0tLS1I4lVCLFlRANpOJsFsZxMzj5+IvcOeZW5n5Q+RLYaXeP55qIruj1jionFEJcjTET7mXt4qX4+/py6NAhevfoyY8//qh2LKEC6dAuRD1TrFYKP/mB3DkL2VSQwbSC38g/Z0KDhn4hkeT8lkZGZhYhagcVQly1qC7d2Lj4Y8Y9NIlD5zMZPXo0rduEEBTWDq228npGoJ8vP6z6UuWkoj7JlSsh6ll5YgoZT7zOItciHsg9SH6FCS+v1tx//xyuu+dpeQmzEM1MWGAQGz77ipvcgwDISk/jzJkMAm+YQuT4uRizc1VOKOqbXLkSoh5Y8grJ//Br3O+6kQN79/GoZzZ7fj0GQNcug4iNnYijo7PKKYUQdeHC6O1/VebqydSuQ/hk1ypyUn/j5+fuo+voB9BZrSqkFA1Jiish6pBSUUHBx9+T8u8FlJnNTJ33NPvPpaMADlodHdxbM3r0FBkHR4hm5M+jt//ZmaUv4DH0Zh6M7MEPaz/ieOZpDn2zGDdnV3bs2EF0dLQKaUVDkNuCQtSRki37SLtmIpkz3+ADcyYjyo6x7/fCqlOnATw8ZT6tHd2lsBKihdEHhXHrhDmMvulh3PVOFJUWM3jwYCbccy/JyclqxxP1QIorIa6SYq5AsVgw/ZbEDwXp3GJI5p3cExQW5+Pl1ZpxY5/g1jH/wN3dR+2oQgiVaDQaunUbwkOTXmaIuz+KorD888/o0L49/3joYTIyMtSOKOqQFFdC1FL58SRWdRrBF+2HMSSyB20fm8gjRzZy/OwZHDRahg4dy+RJ84iI6K52VCFEI6H39CG8fWc2vLaQa4IiMFssvPvB+7Rr147pjz9OUlKS2hFFHZDiSogrVP5bEhkPzeHA4LuJP5PI1KxDbE86Sl5ZMY4GZ4YMvo2BvhFED7wZBweD2nGFEI3QgIED+fnLlfzw0pv069KNkpISFrz1Fu3bteOWwdewcf16FEVRO6aoJenQLsQVKM3K4ZMht/I/cy5rijMpt1QA4OLiQe9e19G370icnd3YmXhE5aRCiKbguiExXDt4CGu2b+XfLzzP0aJc/rd9C/8bPhx/gwtOAQG4tfYnPCRYxsZqQqS4EuISKjJzyf3yZ9Z9/Cnr2nnyzc+rOf+nd4a1cnEn+rp76dixPw4OehWTCiGaiosN3RDo3ppB4/7Fr9u+Y/+JPWSWl0DqaUg9zfljnrz1wn+4Zfw9hIeHN3xocUWkuBLiLxRF4eB/3uXnL74m/vhhdpTnUYoV9lUud3YwEObdmggff8oLSujadbC6gYUQTcqlhm5o1aoNw8ZMZaCphOO/7ebI0e2kpv7G2eJ8Hn9mNo8/M5tOgcHcNOYWbvzbHQwcOBAXFxcVjkJcihRXolkaffvYi46CHOjny/++/AzzqTTMaZkUHD/Nod172HUggUPhXmzbuYOMrCy7ddzcvGjXtheduwwkNKSz7TUWO5e+UO/HIoRoeZwcXejZcxg9ew6joCCX9cvnUmYtJ7W0gN+MZ/ht8UJeX7wQjUZD/569iRl+LYOHDKFPnz6EhITIkC8qU724WrhwIa+++ipGo5GuXbuyYMECYmJiLtp+06ZNxMXFceTIEYKCgnjiiSeYMmWKXZuVK1fy9NNPc+rUKdq1a8eLL77IbbfddlX7FU2LMTuXvjf/k4ik0/jm5uKVdx6Xczkcc9Ky5EgCL86cze53lnK0oogkSym28ZIPVf5H7+BAvy7diB04mN2bdtJ9zOPyZSWEUIWHhy8Brj4M/PvTlJYWkZqYQOpveziRnUxh0Xl2HdjPrgP7ee311wHwcfegd7++9Ordm44dO9KpUyc6duyIn5+ffI81EFWLqy+++IJp06axcOFCBg8ezHvvvceoUaM4evQooaGhVdonJSVx44038uCDD/LJJ5+wbds2pk6dip+fH3fccQcAO3bsYNy4cbzwwgvcdtttfPPNN4wdO5atW7cyYMCAWu1XNF7WohLKTyRTePA46fsOkv7rbxRGdaAo/QzJn7xO1onDpFFButVEprmEC8/ePP36r3bbae3tg4vGAS9HV1q7eeLj4o6DVsfJPUcwFZTIF5IQolFwdnajY48YOvaIYYSicPx/7zAyegBbd+0kIeUUJ4rOc66wgHXr17Nu/Xq7dT0MToR4+1JssVCsd6CVgyPtrXoc9QYMBkd8/Xx55d0FOPXsCIBiKkfjKE8814aqxdX8+fOZNGkSkydPBmDBggWsWbOGRYsWMW/evCrtFy9eTGhoKAsWLACgc+fO7N27l9dee81WXC1YsIDrr7+eWbNmATBr1iw2bdrEggUL+Pzzz2u1X3H1FEXBYrFQXl6O2WzGbDZjMpkoLy/HZDJhMpkoKyujtLTUNhUXF1NUVETh2QwKMrPJy8omPyuHvNxzlAZ4cb6ggKzEJM6XFFGs/OnFx5sq/3OCE1VyOBqccbRa8XX3wtPJBR8XN7yd3XDWO2LMyKTf/U9VWeeM3PoTQjRCGo2GwnPn2ZZwGI3BlT6RPehpsWApKSZXW0Gnnl05tjeBxMyznCkpoKC8jCOZ6bb1s4Fjf97gCVjYqzM6Bwf0ej1dzA64aHU4OegJaOWHh5cXrW++Fo/Wfjhm5+Oic6BL7170GjwQrbcHGp2uof8IGi3Viqvy8nL27dvHzJkz7ebHxsayffv2atfZsWMHsbGxdvNGjhzJkiVLMJvN6PV6duzYwfTp06u0uVCQ1Wa/gK0AuCA/Px+Agj89OVZXrEUl5H/8HUWr1tnmab3ccB09DK+/30rBitUUfrUWS0YOilUBiwXXkUNwv/dGrHmFFH76I0Vrt0OFBaxW9O1Dcb/nJtxuuoYdb3/Ik+8usF3BUQCttwcOga2wFBRRkZOH1VSOAiga0Li5oPV0x6pYsRQUYS0uQ0HBCigOOnB2RHHUU1FcSkVxCVZFwaooWFBQHHRUaKDCbMZS1y8qrVo3oQVcHAzo9QYcLQod/Nvh6+yOt7M7vk4eeHq3Jqdjd/Z++gr39bsF/jKGzKrUHzCZSgkwnsUzP882X2Mx4J6WTHZrf5xLiglNTbFb1ubIIU61jwSg3alEHMxmNBYDYQcre8CnhoZR6uKKX1Ym0X+aD5Dv6UVGYBAGi5XwP82v3LiG4x07U2G1EHj8CI5lZXaLj1vAZCrF+1wurbMy7TL5njpOenAouooK2p88Ybcs7OA+EiM7YtXpCE5LwbW42C5vpn8Aed4+eOTnVclb6uxMalgEQJVlAEkR7aiwWvBJOolHQb7dsjSLBpOpFJfiQkLS0uwyBR09zOl27QFof/IEuooKu7wpYeGUObvQOjMD7/Pn7PLmeXmTGRCIY2lplUxWrZbEDp0A6GlxqPJnnN4mmAqrBdezafhl2/ezy7XoMJlKcTCbaXcqscqf4YkOnVC0WkJSk3EpKbFblhEQSL6XN5555wnIMNrlLXFxIS00HI3VWu2f4em27TEbDERadFXyZvu1psJqwSE3k+AzZ+yWlVocMJlKAYg8cRyt1WKXKTksApOzM/4ZRrzyztstO+/tQ5Z/AE6lJYSlJNvltegcOBnZAYDe1fwZpoWEUOLqThuLpsqyAg9PKqwWrIV5tD19ym6ZxmKg7Pe8oSlJOJeW2i0zZBkp8PTC6/w5/DMz7PIWu7pyJiQMrcVCZOJxu7wAJ9tHYnHQ07GaP8Os1v6c9/HF20KVZSYnJyqsFkymUjoeP2b3HaGxGFAKzmNydKrxd8SFXBUOervviL+e9wvfEcHV/Ble7jtiq8WK39B7CE8+bfcdkX9iN/eO/hsOk/8Pc/JZCo6c4Ez+ec4Unud/mzaT7+vPWU0FJUV5mM/nkG8qptRSjgUFS4WZ8gozey5srBxIzYJU4NA2uwj3OAbwL9dwAPTtQvB65G60Xh4UfLSS0q0JtnYOYUF4PnAbbmOuJX/595h2HsScYgStFrQa3O8cifOQ3ljziyjbnkDxut24DIvC+59/R+vsSF268Hu7XscRU1SSnp6uAMq2bdvs5r/44otKhw4dql0nMjJSefHFF+3mbdu2TQGUs2fPKoqiKHq9Xvn000/t2nz66aeKwWCo9X4VRVGeffZZhcpaRCaZZJJJJplkauJTWlpazQqWWlC9Q/tf+7IoinLJ/i3Vtf/r/Jps80r3O2vWLOLi/hiXxGq1cu7cOXx9fRt1f5yCggJCQkJIS0vDw8ND7Tj1orkfY3M/PpBjbA6a+/GBHGNzcOH4jh49SlBQUL3tR7XiqlWrVuh0uiovq8zKysLf37/adQICAqpt7+DggK+v7yXbXNhmbfYL4OjoiKOj/aVJLy+vix9gI+Ph4dEsf1D+rLkfY3M/PpBjbA6a+/GBHGNz0KZNG9uQOvVBtXcLGgwGoqKiiI+Pt5sfHx/PoEGDql0nOjq6Svu1a9fSt29f9Hr9Jdtc2GZt9iuEEEIIUVOq3haMi4tj/Pjx9O3bl+joaN5//31SU1Nt41bNmjWL9PR0li9fDsCUKVN45513iIuL48EHH2THjh0sWbLE9hQgwOOPP84111zDyy+/zJgxY/juu+/45Zdf2Lp1a433K4QQQghRa/XWm6uG3n33XSUsLEwxGAxKnz59lE2bNtmWTZgwQRk6dKhd+40bNyq9e/dWDAaDEh4erixatKjKNr/66iulY8eOil6vVzp16qSsXLnyivbbnJSVlSnPPvusUlZWpnaUetPcj7G5H5+iyDE2B839+BRFjrE5aKjj0yhKfT6LKIQQQgjRsqjW50oIIYQQojmS4koIIYQQog5JcSWEEEIIUYekuBJCCCGEqENSXDUDCxcuJCIiAicnJ6KiotiyZcsl22/atImoqCicnJxo27YtixcvbqCkV27evHn069cPd3d3Wrduza233srx48cvuc7GjRvRaDRVpt9++62BUtfcnDlzquQMCAi45DpN6fwBhIeHV3s+HnnkkWrbN4Xzt3nzZm6++WaCgoLQaDR8++23dssVRWHOnDkEBQXh7OzMsGHDOHLkyGW3u3LlSrp06YKjoyNdunThm2++qacjuLRLHZ/ZbObJJ5+ke/fuuLq6EhQUxP3338/Zs2cvuc1ly5ZVe17L/vLOzIZyuXM4ceLEKlkHDhx42e02lnMIlz/G6s6HRqPh1Vdfveg2G9N5rMnvB7V+FqW4auK++OILpk2bxuzZs0lISCAmJoZRo0aRmppabfukpCRuvPFGYmJiSEhI4KmnnuKxxx5j5cqVDZy8ZjZt2sQjjzzCzp07iY+Pp6KigtjYWIqLiy+77vHjxzEajbYpMjKyARJfua5du9rlPHz48EXbNrXzB7Bnzx6747swgO/f/va3S67XmM9fcXExPXv25J133ql2+SuvvML8+fN555132LNnDwEBAVx//fUUFhZedJs7duxg3LhxjB8/noMHDzJ+/HjGjh3Lrl276uswLupSx1dSUsL+/ft5+umn2b9/P6tWreLEiRPccsstl92uh4eH3Tk1Go04OTnVxyFc1uXOIcANN9xgl3X16tWX3GZjOodw+WP867n46KOP0Gg03HHHHZfcbmM5jzX5/aDaz2K9DvQg6l3//v2VKVOm2M3r1KmTMnPmzGrbP/HEE0qnTp3s5j388MPKwIED6y1jXcrKylKAS45LtmHDBgVQzp8/33DBaunZZ59VevbsWeP2Tf38KYqiPP7440q7du0Uq9Va7fKmdP4URVEA5ZtvvrF9tlqtSkBAgPLSSy/Z5pWVlSmenp7K4sWLL7qdsWPHKjfccIPdvJEjRyp33XVXnWe+En89vurs3r1bAZSUlJSLtlm6dKni6elZt+HqSHXHOGHCBGXMmDFXtJ3Geg4VpWbnccyYMcp11113yTaN+Tz+9feDmj+LcuWqCSsvL2ffvn3ExsbazY+NjWX79u3VrrNjx44q7UeOHMnevXsxm831lrWu5OfnA+Dj43PZtr179yYwMJDhw4ezYcOG+o5Wa4mJiQQFBREREcFdd93F6dOnL9q2qZ+/8vJyPvnkEx544IHLvvC8qZy/v0pKSiIjI8PuPDk6OjJ06NCL/lzCxc/tpdZpLPLz89FoNJd932pRURFhYWEEBwczevRoEhISGiZgLW3cuJHWrVvToUMHHnzwQbKysi7Zvimfw8zMTH788UcmTZp02baN9Tz+9feDmj+LUlw1YTk5OVgsliovnPb396/yYuoLMjIyqm1fUVFBTk5OvWWtC4qiEBcXx5AhQ+jWrdtF2wUGBvL++++zcuVKVq1aRceOHRk+fDibN29uwLQ1M2DAAJYvX86aNWv44IMPyMjIYNCgQeTm5lbbvimfP4Bvv/2WvLw8Jk6ceNE2Ten8VefCz96V/FxeWO9K12kMysrKmDlzJvfcc88lX/TbqVMnli1bxvfff8/nn3+Ok5MTgwcPJjExsQHT1tyoUaP49NNPWb9+Pa+//jp79uzhuuuuw2QyXXSdpnoOAT7++GPc3d25/fbbL9musZ7H6n4/qPmzqOq7BUXd+OsVAEVRLnlVoLr21c1vbP7xj39w6NAhu/dEVqdjx4507NjR9jk6Opq0tDRee+01rrnmmvqOeUVGjRpl+//u3bsTHR1Nu3bt+Pjjj4mLi6t2naZ6/gCWLFnCqFGjCAoKumibpnT+LuVKfy5ru46azGYzd911F1arlYULF16y7cCBA+06hA8ePJg+ffrw9ttv89Zbb9V31Cs2btw42/9369aNvn37EhYWxo8//njJAqSpncMLPvroI+69997L9p1qrOfxUr8f1PhZlCtXTVirVq3Q6XRVqumsrKwqVfcFAQEB1bZ3cHDA19e33rJerUcffZTvv/+eDRs2EBwcfMXrDxw4UPV/WdWEq6sr3bt3v2jWpnr+AFJSUvjll1+YPHnyFa/bVM4fYHva80p+Li+sd6XrqMlsNjN27FiSkpKIj4+/5FWr6mi1Wvr169dkzmtgYCBhYWGXzNvUzuEFW7Zs4fjx47X62WwM5/Fivx/U/FmU4qoJMxgMREVF2Z6+uiA+Pp5BgwZVu050dHSV9mvXrqVv377o9fp6y1pbiqLwj3/8g1WrVrF+/XoiIiJqtZ2EhAQCAwPrOF3dM5lMHDt27KJZm9r5+7OlS5fSunVrbrrppitet6mcP4CIiAgCAgLszlN5eTmbNm266M8lXPzcXmodtVworBITE/nll19qVdgrisKBAweazHnNzc0lLS3tknmb0jn8syVLlhAVFUXPnj2veF01z+Plfj+o+rNY467volFasWKFotfrlSVLlihHjx5Vpk2bpri6uirJycmKoijKzJkzlfHjx9vanz59WnFxcVGmT5+uHD16VFmyZImi1+uVr7/+Wq1DuKT/+7//Uzw9PZWNGzcqRqPRNpWUlNja/PUY33jjDeWbb75RTpw4ofz666/KzJkzFUBZuXKlGodwSf/85z+VjRs3KqdPn1Z27typjB49WnF3d2825+8Ci8WihIaGKk8++WSVZU3x/BUWFioJCQlKQkKCAijz589XEhISbE/LvfTSS4qnp6eyatUq5fDhw8rdd9+tBAYGKgUFBbZtjB8/3u6p3m3btik6nU556aWXlGPHjikvvfSS4uDgoOzcubNRHZ/ZbFZuueUWJTg4WDlw4IDdz6XJZLro8c2ZM0f5+eeflVOnTikJCQnK3//+d8XBwUHZtWtXgx+folz6GAsLC5V//vOfyvbt25WkpCRlw4YNSnR0tNKmTZsmcw4V5fJ/TxVFUfLz8xUXFxdl0aJF1W6jMZ/Hmvx+UOtnUYqrZuDdd99VwsLCFIPBoPTp08dumIIJEyYoQ4cOtWu/ceNGpXfv3orBYFDCw8Mv+kPVGADVTkuXLrW1+esxvvzyy0q7du0UJycnxdvbWxkyZIjy448/Nnz4Ghg3bpwSGBio6PV6JSgoSLn99tuVI0eO2JY39fN3wZo1axRAOX78eJVlTfH8XRgu4q/ThAkTFEWpfAT82WefVQICAhRHR0flmmuuUQ4fPmy3jaFDh9raX/DVV18pHTt2VPR6vdKpUyfVCspLHV9SUtJFfy43bNhg28Zfj2/atGlKaGioYjAYFD8/PyU2NlbZvn17wx/c7y51jCUlJUpsbKzi5+en6PV6JTQ0VJkwYYKSmppqt43GfA4V5fJ/TxVFUd577z3F2dlZycvLq3Ybjfk81uT3g1o/i5rfAwohhBBCiDogfa6EEEIIIeqQFFdCCCGEEHVIiishhBBCiDokxZUQQgghRB2S4koIIYQQog5JcSWEEEIIUYekuBJCCCGEqENSXAkhhBBC1CEproQQQggh6pAUV0IIIYQQdUiKKyGEEEKIOiTFlRBCCCFEHfp/c7dV4zVyQ0EAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Histogram of sample means (blue)\n",
"sns.histplot(gaussian_sample_means, stat=\"density\", label=\"hist\")\n",
"\n",
"# Estimated PDF of sample means (red)\n",
"sns.kdeplot(\n",
" data=gaussian_sample_means,\n",
" color=\"crimson\",\n",
" label=\"kde\",\n",
" linestyle=\"dashed\",\n",
" fill=True,\n",
")\n",
"\n",
"# Gaussian curve with estimated mu and sigma (black)\n",
"plt.plot(\n",
" x_range,\n",
" norm.pdf(x_range, loc=mu_sample_means, scale=sigma_sample_means),\n",
" color=\"black\",\n",
" label=\"gaussian\",\n",
")\n",
"\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "9564547c",
"metadata": {},
"source": [
"Both curves look almost identical!\n",
"\n",
"Another way of checking for normality is to perform a QQ plot of the sample means. The points in this plot should resemble a straight line if the distribution of the data is Gaussian:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "62f22356",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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jR+GZZ2zfLgsQQDzL6UQLtnCF/DzEYlbRweaxJpP1OO6428VROebumH///ZdVq1YxaNCgmx578eJFKlasSPny5enQoQP79u3L9PikpCQSEhKsPiIiIq5w46WXfv0gPt72cSU5xUZCaMEW4gkgnHUZAojJlPZ5/nnPuNvFUTkmhHzxxRf4+/vT7SY/zerVqzN37lyWL1/OwoULyZ8/P02aNOHQoUN2+0yZMoXAwEDLJzg42Nnli4iI2H2DbXoV+IetNKMe+zhFSVqyia00z3DctaDx5ptw5EjaXTALFqT9MybGswMIeNAtuiaTiaVLl9LlhtcN36h69eqEhoby4YcfOjRuamoq9erVo3nz5nzwwQc2j0lKSiIpKcmynZCQQHBwsG7RFRERp7G+1da+6hxgPWEEc4x/qEAo0RziTqtjXnkFWrVy3m21zpTrbtHdunUrBw8eZNGiRQ739fLyomHDhpnOhPj5+eHn53c7JYqIiGRq06abB5D67GEtbSjBGQ5QnVCiOU55y/5rC00nTPC88HErcsTlmFmzZlG/fn1q167tcF/DMNi/fz9lPfX+JBERybXM5rTnfDz0EHSwvZ7UoiUb2UgIJTjDDzSkGVszBBDw7IWmjnLrTMjFixc5fPiwZTsmJob9+/dTrFgxKlSoAKRN6yxevJh33nnH5hj9+vWjXLlyTJkyBYCJEyfywAMPUK1aNRISEvjggw/Yv38/H330ketPSERE5P9FRsLgwXDmzM2P7UwUi+iFH8l8y4N0IYrLXv6Qev2Y8uXTAoinr/NwhFtDyJ49ewgJCbFsjxw5EoD+/fszd+5cAL7++msMw6B37942x4iNjcXL6/qEzvnz5xk8eDAnT54kMDCQunXrsmXLFu677z7XnYiIiMgNIiPhJo+0shjAHD7ncbxJJZKu9GEBASXzc+of2LXL+Y9V9yQeszDVk+jdMSIicqvMZqhYMe0ttjfzHO/yLqMAmM1jDOZTUk0+Hn9rbWYc+R2aI9aEiIiI5BRbt2YlgBhM5hVLAHmbUQxiFkHBOTuAOCpH3B0jIiKSU9h6WdyNvDAznWE8xQwAxvA6XmNeYmOYKVdecsmMQoiIiIgTZfJECPKRzDz68TCLSMXE03zM6uAhxEzOW+HjGoUQERERJ4mMhPHjbe8rwGUi6E5b1pJMPvryJYtNvVgyLW8GEFAIERERcQqzGYYPt72vCOdYSQeasINLFKQbkewtHs6ST/PO+g9bFEJEREScYOtW209ELUMca2lDbX7mHEXo5ruKkLGNWT02786AXKMQIiIi4gS27oipzN9EE0oV/iaOMoSzjhdn38sjj2R/fZ5IIUREROQ2RUbC009bt9XkV9YTRhBx/E1lQonmb6pQrpx7avRECiEiIiK3wdbTUe/ne1bTjmKc4xfuIZx1xBFE+fJpTz6VNHpYmYiIyC2ytRi1NdF8SyuKcY6dPEALNhNHEABPPKF1IDdSCBEREblF6RejdmcJq2hPIS6zjjBas4FzFLPsr1bNDUV6MIUQERGRW7Rs2fWvH+czFtELX66yiJ50ZAWXKWR1fNmy2Vygh1MIERERuQVmM8yenfb1C0zlMwbjTSozGUwfFnAVX6vjg4O1HiQ9hRAREZEsMpvh229h7Fi44w5ISDCYygtM5SUAXmcMQ5hBKtYLP0wmmDZN60HS090xIiIiWbBkCQwaBAkJadtemPmMJ3mcWQCM5i3eYXSGfoULwxdf5O0no9qjECIiInITL7wAb711fduXJL7iEXoQgRkvBvMpsxlks29UFLRqlT115jQKISIiIjZcu/QyeTJs23a9vRAXWUpXQtlAEr70ZiFLsT3NUbw4tGyZPfXmRAohIiIi6SxZAv36wZUr1u3FOMMq2vMAu7hIIboQxbe0tjvOs89qHUhmtDBVRETkBs8/Dw89lDGABHGcLTTnAXZxhmI8yHeZBpCAgLQFrGKfZkJERET+36hR8O67Gdurcoj1hFGZIxyjHGGs5wA1Mh1r1izNgtyMZkJERESA0aNtB5Da7GcbTanMEQ5RlaZsu2kAGT0aevRwUaG5iEKIiIjkeYsXwzvvZGxvwjY20ZLSnGIfdWjKNv6hUqZjjRplfSeN2KfLMSIikqeZzfD44xnb27KaJfSgIFfYSlM6soJ4itgdJyAAPv88bT2JZI1CiIiI5Gl9+lx/ANk1D7OQefQjHymsoh0PsZgrFMzQN1++tEsvrVql3YqrNSCOUQgREZE8a9Qo+OYb67an+JjpDMMLg6/owwDmkkI+m/2//lpPQr0dWhMiIiJ5UsaFqAZj+R8fMxQvDD5kGH350mYAKV4cIiIUQG6XQoiIiOQ5X39tvRDVRCrvMpL/MQ6AibzKs3yAke7XZNeusGED/PuvAogz6HKMiIjkKc89l/ZG22u8SWEWg+jPPACGM40PGJ6h38SJ8Oqr2VRkHqEQIiIiecZ998Hu3de3/UhkEb3ozHJS8GYgs/mSfhn6lSihp5+6gkKIiIjkCc89Zx1A/ElgGZ0JYROJ+NGTb1hBJ5t9P/lEd764gkKIiIjkegsXWl+CKcF/rKEtDdhLAv50YjmbaWmzr55+6jpamCoiIrna88+nPQvkmvIcZSvNaMBe/qMEIWy0G0D09FPX0kyIiIjkWukXod7JQaIJpQJHiSWYUKL5k7ts9l24EB5+OHvqzKsUQkREJFfq2BFWrry+XY+9rKUNJTnNAaoTxnqOEWyz74gRCiDZQZdjREQk1zCbYc0aKFzYOoC0YBMbCaEkp9lDfZqzxW4AadgQ3nsvmwrO4xRCREQkV4iMTAsf7drBpUvX2zuynLW0IYALbKQlD/Idpylpc4znnoMffsimgkWXY0REJOeLjITu3TO292UesxmID2aW0YleLCKJ/DbHOH8eAgNdW6dY00yIiIjkaMnJtm+hfZb3mUd/fDAzl/50J8JuAOnUSQHEHRRCREQkx4qMBD8/MIwbWw0m8irvMwKA9xjBQGZjtjP536ABLFvm8lLFBoUQERHJkWxdgjGRyoc8w6tMBuAVJjOSdzO8iO6adu2sn6Iq2UtrQkREJMcxm+HRR63bfLjKXAbwCAtIxcRQPmIGT9kdo359WLXKxYVKpjQTIiIiOc5338GVK9e3C3CZKLrwCAu4ig+P8FWmAaRDB9izJxsKlUwphIiISI7Tps31rwM5zzrCac9qLlOAzizja3rb7fvcc7BiRTYUKTelyzEiIpKjBAdDamra16X4l3WEU4efOE8gHVjJdpra7OfjAwsWwEMPZWOxkinNhIiISI5w5Qr4+sKxY2nbFTnCNppSh584SWlasNluAHn5ZUhMVADxNAohIiLi8Tp1goIF4erVtO27+Z3tNKEah4mhEk3Zxs/Uttm3c2d47TXw9s7GgiVLdDlGREQ82h13QEzM9e2G/MAa2lKcs/xKTcJZxwnK2ew7ciS88042FSoOc+tMyJYtW+jYsSNBQUGYTCaioqKs9g8YMACTyWT1eeCBB246bkREBDVq1MDPz48aNWqwdOlSF52BiIi4UokS1gGkFRv4jgcpzlm+536as8VuAJk9WwHE07k1hFy6dInatWszffp0u8e0adOGuLg4y2f16tWZjrlz50569epF3759+emnn+jbty89e/Zk165dzi5fRERcJDk5bSHpmTPX27oSySraU5hLRNOa1mzgHMVs9i9SBB57LHtqlVtnMgzrh926i8lkYunSpXTp0sXSNmDAAM6fP59hhiQzvXr1IiEhgTVr1lja2rRpQ9GiRVm4cGGWxkhISCAwMJD4+HgCAgKy/L1FROT2Pf88vP22ddtAZvEpg/EmlSV05xG+Ihk/u2OkpGgNiLs48jvU4xembtq0iVKlSnHnnXfyxBNPcOrUqUyP37lzJ2FhYVZt4eHh7Nixw26fpKQkEhISrD4iIpK9zGZo2DBjABnNW8zicbxJ5XMG0YtFmQaQBQsUQHIKjw4hbdu25auvvuK7777jnXfeYffu3Tz44IMkJSXZ7XPy5ElKly5t1Va6dGlOnjxpt8+UKVMIDAy0fIKDg512DiIicnNLlqRdfrF+iqnB64zhLV4AYCov8ASfkYr9hNGwIfS2/5wy8TAeHUJ69epF+/btueeee+jYsSNr1qzhzz//ZNVNHvZvMpmstg3DyNB2ozFjxhAfH2/5HD161Cn1i4jIzb3wQsbnd3hhZgZDGMMbALzIG7zEVMD+3+WdOsEPP7iwUHG6HHWLbtmyZalYsSKHDh2ye0yZMmUyzHqcOnUqw+zIjfz8/PDzsz+1JyIirrF4Mbz1lnVbPpKZz6P0ZDFmvBjCDD7nCbtjeHvDhQtQoICLixWn8+iZkPTOnDnD0aNHKVu2rN1jGjVqRHR0tFXb+vXrady4savLExERB5jN0LOndVtBLrGCjvRkMcnkoxeLMg0gxYqlLUJVAMmZ3DoTcvHiRQ4fPmzZjomJYf/+/RQrVoxixYoxYcIEunfvTtmyZTly5Agvv/wyJUqUoGvXrpY+/fr1o1y5ckyZMgWA4cOH07x5c6ZOnUrnzp1ZtmwZGzZsYNu2bdl+fiIiYp9Put9ARTnLKtrTiO+5SCG6spQNhNrtX7Ik3OReBfFwbp0J2bNnD3Xr1qVu3boAjBw5krp16/Lqq6/i7e3NL7/8QufOnbnzzjvp378/d955Jzt37sTf398yRmxsLHFxcZbtxo0b8/XXXzNnzhzuvfde5s6dy6JFi7j//vuz/fxERMS29Mv0ynKCzbSgEd9zlqK0ZkOmAaR9ewWQ3MBjnhPiSfScEBER10kfQO7gL6IJ5Q5iOEFZwljPb9xjt//XX0OvXi4uUm6ZI79Dc9TCVBERybmuXEl7Cd2NavEz6winLCc5TBVCieYIle2OoYeQ5S45amGqiIjkTO3aZQwgjdjBZlpQlpP8xL00ZZvdAFKhAhiGAkhuo5kQERFxqYIF02ZBbhTOWiLpRkGusI0mdGQF5ylqs/+ZM2l3wUjuo5kQERFxiStX0tZ/pA8gPVnEcjpRkCuspi1hrLcbQCIiFEByM4UQERFxuk6dMl5+AXiSGSykN75cZSEP04UormDjQNIeZNatm4sLFbfS5RgREXGqSpXgn3/StxqMYQqvMxaAj3mKZ/jQ7ntgFi6EHj1cWqZ4AIUQERFxGtuv6TJ4m9GM4l0AJvMKrzIJe++BadsWHn7YZSWKB1EIERERp7AVQLxJ4VMGM5A5ADzHu0zjObtjBATA6tWuqlA8jUKIiIjcNlsBxI9EFtKbrkRhxotBzOILBtgdw98f4uNdV6N4Hi1MFRGR21KnTsa2wlxgFe3pShRJ+NKdiEwDyNChkJDgshLFQ2kmREREbtnFi/DTT9ZtxTnNatpxH7u5QGE6sZxNhNgdIykJfH1dXKh4JIUQERG5ZTe8TxSAchxjPWHU4ACnKU4b1rKXBnb76+1leZsux4iIyC1Jvw6kGn+ynSbU4ABHKU8zttoNINcewy55m0KIiIg45OTJjAGkLj+yjaZUJJaD3EkTtvMHd9vsf/68reeISF6kyzEiIpJltt4D04wtrKAjgSTwI3Vpw1r+o5TN/pr9kBtpJkRERLLE1ntg2rOSdYQTSAKbaU4IGxVAJMsUQkRE5KZsPQekD18RRRcKkMgKOtCGtSQQaLN/UpKLC5QcSSFEREQyZSuADONDvuJRfDDzJY/SjUgSKWCz/8iRugVXbFMIERERuzIGEINXmciHPAvA+zxLf74ghXw2+9etC++849oaJefSwlQREbGpeXPrbROpTGMEz/IhAK8ykcmMw96L6Pz84McfXVyk5GgKISIikkH6GRAfrjKbgfRlPpB2OeYjhmU6RmKiq6qT3EIhRERErKQPIPm5wjf0pCMrScGb/nzBAh6x29/HB65edXGRkitoTYiIiFikDyABxLOWNnRkJVfITxeiMg0gcXEKIJJ1mgkRERH++w9KpXu8R0lOsZY21GMf8QTQkRVspbntAdBzQMRxCiEiInlcYCAkJFi3VeAf1hPGXfzJv5SiDWvZT127YyiAyK1QCBERycNsPQOkOgdYTxjBHOMIFQklmsNUszuGAojcKq0JERHJo2wFkAbsZivNCOYYv3M3TdmmACIuoxAiIpIH2QogIXzHdzxICc7wAw1pzhaOU97uGAogcrsUQkRE8piaNTO2dSaKNbTFn4t8y4O04lvOUMLuGAog4gxaEyIikofkz5/xZXIDmMPnPI43qUTSlT4sIIn8dsdQABFn0UyIiEgeYTJlDCDP8S5zGIg3qczmMXryjQKIZBuFEBGRPMDWi+gm8wrvMgqAtxnFIGZhzmSCXAFEnE0hREQkl0sfQLww8zFP8wqvAfASU3iet7D3Irp771UAEdfQmhARkVwsfQDJRzLz6MfDLCIVE0/xCZ/ypN3+Fy5A4cIuLlLyLIUQEZFcKn0AKcglltCDtqwlmXz05Uu+oZfd/pr9EFdTCBERyYXSB5AinGMlHWjCDi5RkG5Esp5wu/0VQCQ7KISIiOQy6QNIGeJYRzj38gvnKEJ7VrGTxnb7K4BIdlEIERHJRdIHkMr8TTShVOFv4ihDOOv4hXvt9lcAkeyku2NERHKJ9AGkJr+yjaZU4W/+4g6ask0BRDyKQoiISA4XE5MxgNzP92yhOUHE8Qv30JRt/E0Vu2MogIg76HKMiEgO5u0NqanWbaGsZyldKcRldtCI9qziPEXtjqEAIu6imRARkRzIbE6b/UgfQHqwmJV0oBCXWUcYoUQrgIjHUggREclhvvkGfGzMYz/OZyyiF75cZRE96cgKLlPI7jgKIOJuCiEiIjlIx47Qy8bzxV5gKp8xGC8MZjKYPizgKr52x1EAEU+gNSEiIjlEcDAcO5a+1WAqL/ICbwHwOmMYy2vYew8MKICI51AIERHJATK+BTftRXQzeZLHmQXAaN7iHUZnOo4CiHgSt16O2bJlCx07diQoKAiTyURUVJRl39WrV3nxxRepVasWhQoVIigoiH79+nHixIlMx5w7dy4mkynDJzEx0cVnIyLiGrYCiC9JLKIXjzMLM14MZJYCiOQ4bg0hly5donbt2kyfPj3DvsuXL/Pjjz8ybtw4fvzxRyIjI/nzzz/p1KnTTccNCAggLi7O6pM/f35XnIKIiEvZCiCFuMhKOtCDCJLw5SEWM4eBdseoVk0BRDyTWy/HtG3blrZt29rcFxgYSHR0tFXbhx9+yH333UdsbCwVKlSwO67JZKJMmTJOrVVEJLvZCiDFOMNq2nE/P3CRQnRmGd/Ryu4YCxZA794uLFLkNuSoNSHx8fGYTCaKFCmS6XEXL16kYsWKmM1m6tSpw+TJk6lbt67d45OSkkhKSrJsJyQkOKtkEZFbYiuABHGc9YRRk985QzHasobd3Gd3jJSUtIeZiXiqHHOLbmJiIi+99BJ9+vQhICDA7nHVq1dn7ty5LF++nIULF5I/f36aNGnCoUOH7PaZMmUKgYGBlk9wcLArTkFEJEtsBZCqHGI7TajJ7xyjHM3YmmkAMQwFEPF8JsPwjCuFJpOJpUuX0qVLlwz7rl69ykMPPURsbCybNm3KNISkl5qaSr169WjevDkffPCBzWNszYQEBwcTHx/v0PcSEbldtgJIbfazjnBKc4pDVCWUaP6hks3+P/8MtWq5tkaRzCQkJBAYGJil36Eefznm6tWr9OzZk5iYGL777juHQ4GXlxcNGzbMdCbEz88PPz+/2y1VROS22AogTdjGSjpQhHj2UYc2rOUUpW3294z/pRTJOo++HHMtgBw6dIgNGzZQvHhxh8cwDIP9+/dTtmxZF1QoInL7Dh+2HUDaspr1hFGEeLbSlBA2KoBIruLWmZCLFy9y+PBhy3ZMTAz79++nWLFiBAUF0aNHD3788UdWrlyJ2Wzm5MmTABQrVgxf37THEffr149y5coxZcoUACZOnMgDDzxAtWrVSEhI4IMPPmD//v189NFH2X+CIiI3YSt8APRmAV/Qn3yksJL29OQbrlDQ5rEKIJJTuTWE7Nmzh5CQEMv2yJEjAejfvz8TJkxg+fLlANSpU8eq38aNG2nZsiUAsbGxeHldn9A5f/48gwcP5uTJkwQGBlK3bl22bNnCfffZX8AlIpLd4uPB3o1+T/MRH/IMXhh8RR8GMJcU8tk8VgFEcjKPWZjqSRxZVCMi4qiqVeGvv2ztMXiF/zGZVwH4kGEM530MO1fO9be3eCJHfod69JoQEZHc5o47bAcQE6m8x3OWADKRV3mWDxRAJFfz+LtjRERyizp1ICYmY7s3KcxiEP2ZB8BwpvEBw+2OowAiuYVCiIhINihZEk6fztjuRyKL6EVnlpOCNwOZzZf0szuOAojkJgohIiIuZu8OGH8SWEZnQthEIn705BtWYP8lnQogktsohIiIuJC9AFKC/1hDWxqwlwT86cgKttDC7jgKIJIbaWGqiIiL2AsgwcSylWY0YC+nKElLNtkNINOmKYBI7qWZEBERF7AXQO7iD6IJJZhjxBJMKNH8yV02j9VbcCW300yIiIiT2Qsg9djLVpoRzDEOUJ0mbLcbQPQWXMkLFEJERJzIXgBpwSY2EkJJTrOH+jRnC8cIznDcrl26/CJ5hy7HiIg4ib0A0pHlfENP8pPERlrSmWVcIOOTJBU+JK/RTIiIiBPYCyB9mUck3chPElF0pi1rFEBE/p9CiIjIbbIXQJ7lfebRHx/MzGEAPVhCEvkzHKcAInmVQoiIyG2wHUAMJvIq7zMCgHd5jkHMwmzjCrgCiORlWhMiInKLbAUQE6l8yDMM5WMAxvI/XudlIOPBCiCS1zk8E3L06FGOHTtm2f7hhx8YMWIEn376qVMLExHxZLYCiA9Xmc+jDOVjUjHxFB/zOmNRABGxzeEQ0qdPHzZu3AjAyZMnCQ0N5YcffuDll19m0qRJTi9QRMTT2AogBbhMFF3ow0Ku4sMjfMUMnrLZXwFEJI3DIeTXX3/lvvvuA+Cbb77hnnvuYceOHSxYsIC5c+c6uz4REY9iK4AEcp51hNOe1VymAJ1Zxtf0ttlfAUTkOofXhFy9ehU/Pz8ANmzYQKdOaW98rF69OnFxcc6tTkTEg9gKIKX4l3WEU4efOE8gHVjJdpra7K8AImLN4ZmQmjVrMmPGDLZu3Up0dDRt2rQB4MSJExQvXtzpBYqIeAJbAaQiR9hGU+rwEycpTQs2K4CIOMDhEDJ16lRmzpxJy5Yt6d27N7Vr1wZg+fLllss0IiK5ia0AUoPf2E4TqnGYGCrRlG38TG2b/RVARGwzGYbjfzzMZjMJCQkULVrU0nbkyBEKFixIqVKlnFqgOyQkJBAYGEh8fDwBARmfbCgieYetAHIfu1hNO4pzll+pSTjrOEE5m/0VQCSvceR36C09rMwwDPbu3cvMmTO5cOECAL6+vhQsWPBWhhMR8ThXrtgOIK3YwLe0ojhn+Z77ac4WBRCRW+TwwtR//vmHNm3aEBsbS1JSEqGhofj7+/Pmm2+SmJjIjBkzXFGniEi26dABVq3K2N6NCBbQBz+SiaY1XVnKJQrbHEMBROTmHJ4JGT58OA0aNODcuXMUKFDA0t61a1e+/fZbpxYnIpLdAgNtB5CBzOIbeuJHMkvoTgdWKoCI3CaHZ0K2bdvG9u3b8fX1tWqvWLEix48fd1phIiLZzccHzOaM7aN5i7d4AYDPeJwhzCAVb5tjKICIZJ3DMyGpqamYbfwpPXbsGP7+/k4pSkQku1WqZCuAGLzOGEsAeYMXGcynCiAiTuJwCAkNDWXatGmWbZPJxMWLFxk/fjzt2rVzZm0iItkiPh7++ce6zQszM3mSMbwBwAtM/f+vbb42VwFE5BY4fIvuiRMnCAkJwdvbm0OHDtGgQQMOHTpEiRIl2LJli27RFZEc5eJFSD+J60sSX9KXnizGjBdPMpNZPG53DAUQkesc+R3q8JqQoKAg9u/fz8KFC/nxxx9JTU1l0KBBPPLII1YLVUVEPF2DBrB3r3VbIS4SSTfCiCaZfPRhARH0sDuGAojIrbulh5XldpoJEcn9AgMhIcG6rShnWUV7GvE9FylEV5aygVC7Y+hvT5GMXDoTMm/evEz39+vXz9EhRUSyla2HkJXlBOsIpxa/cpaitGM1u3jA7hgKICK3z+GZkBsf1Q5pb9W9fPmy5YmpZ8+edWqB7qCZEJHcy1YAuYO/iCaUO4jhBGUJYz2/cY/N/n//DZUru7hIkRzMpTMh586dy9B26NAhnnrqKZ5//nlHhxMRyTa2AkgtfmYd4ZTlJIepQijRHMF2yrh8GbT0TcR5bundMelVq1aNN954g+HDhztjOBERp7MVQBqznc20oCwn+Yl7aco2uwGkUycFEBFnc0oIAfD29ubEiRPOGk5ExGlsBZBw1hJNKEU5zzaa0ILN/EsZm/3r1YNly1xcpEge5PDlmOXLl1ttG4ZBXFwc06dPp0mTJk4rTETEGWwFkF58zZf0JR8prKYtPVjCFWy/BbxSpYy38YqIczgcQrp06WK1bTKZKFmyJA8++CDvvPOOs+oSEblttgLIk8zgY57GC4OFPEx/vuAqvhkPJO05Irt3u7hIkTzM4RCSmprqijpERJwqYwAxGMMUXmcsAB/zFM/wod33wFy4AIVtvyRXRJzE4RAiIuLpbAWQtxnNKN4FYDKv8CqT0HtgRNwrSyFk5MiRWR7w3XffveViRERuV/oA4k0KnzKYgcwB4DneZRrP2e2vACKSfbIUQvbt25elwUy2LsCKiGST9H8F+ZHIQnrTlShS8GYQs5hHf7v9FUBEsleWQsjGjRtdXYeIyG1JH0AKc4EoutCK70jEj14sYjmd7fZXABHJfloTIiI5XvoAUpzTrKEtDdnDBQrTieVsIsRufwUQEfe4pRCye/duFi9eTGxsLMnJyVb7IiMjnVKYiEhWpA8g5TnKesK4mz84TXHasJa9NLDbXwFExH0cfmLq119/TZMmTfj9999ZunQpV69e5ffff+e7774jMDDQFTWKiNiUPoBU40+20ZS7+YOjlKcZWxVARDyYwyHk9ddf57333mPlypX4+vry/vvvc+DAAXr27EmFChVcUaOISAbpA0hdfmQbTalILAe5kyZs5w/utttfAUTE/RwOIX/99Rft27cHwM/Pj0uXLmEymXjuuef49NNPnV6giEh66QNIM7awkRBK8R97qUcztnIU+/9TpAAi4hkcDiHFihXjwoULAJQrV45ff/0VgPPnz3P58mWHxtqyZQsdO3YkKCgIk8lEVFSU1X7DMJgwYQJBQUEUKFCAli1b8ttvv9103IiICGrUqIGfnx81atRg6dKlDtUlIp4rfQBpz0rWEU4gCWyiBSFs5D9K2e2vACLiORwOIc2aNSM6OhqAnj17Mnz4cJ544gl69+5Nq1atHBrr0qVL1K5dm+nTp9vc/+abb/Luu+8yffp0du/eTZkyZQgNDbWEIFt27txJr1696Nu3Lz/99BN9+/alZ8+e7Nq1y6HaRMTzpA8gjzCfKLpQgESW05G2rOECAXb7K4CIeBaTYWTtj+X+/fupU6cOZ8+eJTExkaCgIFJTU3n77bfZtm0bVatWZdy4cRQtWvTWCjGZWLp0qeUFeYZhEBQUxIgRI3jxxRcBSEpKonTp0kydOpUnn3zS5ji9evUiISGBNWvWWNratGlD0aJFWbhwYZZqSUhIIDAwkPj4eAIC7P+FJiLZJ30AeYYP+IDhAMyjL4OYRQr57PZXABHJHo78Ds3yTEi9evWoX78+ixYtolChQmmdvbx44YUXWL58Oe++++4tBxBbYmJiOHnyJGFhYZY2Pz8/WrRowY4dO+z227lzp1UfgPDw8Ez7JCUlkZCQYPUREc9hHUAMxjPBEkDe51kGMFcBRCQHynII2b59O/Xq1eOll16ibNmyPProoy59kurJkycBKF26tFV76dKlLfvs9XO0z5QpUwgMDLR8goODb6NyEXGmGwOIiVTeZzgTmAjAq0xkBNMwMvmrTAFExHNlOYQ0atSIzz77jJMnT/LJJ59w7NgxWrduTZUqVXjttdc4duyYSwpM/z4awzBu+o4aR/uMGTOG+Ph4y+fo0aO3XrCIOM2Nf2x9uMoX9OdZPgRgGB8ymVex9yZcUAAR8XQOL0wtUKAA/fv3Z9OmTfz555/07t2bmTNnUrlyZdq1a+e0wsqUKQOQYQbj1KlTGWY60vdztI+fnx8BAQFWHxFxrxsDSH6uEEk3+jKfq/jwCPP5iGGZ9lcAEfF8DoeQG1WpUoWXXnqJsWPHEhAQwLp165xVF5UrV6ZMmTKWO3EAkpOT2bx5M40bN7bbr1GjRlZ9ANavX59pHxHxHFeuWAeQAOJZSxs6spIr5KcLUSzgkUzHUAARyRlu+QV2mzdvZvbs2URERODt7U3Pnj0ZNGiQQ2NcvHiRw4cPW7ZjYmLYv38/xYoVo0KFCowYMYLXX3+datWqUa1aNV5//XUKFixInz59LH369etHuXLlmDJlCgDDhw+nefPmTJ06lc6dO7Ns2TI2bNjAtm3bbvVURSSbtG0La9de3y7JKdbShnrsI54AOrCSbTTLdAwFEJEcxHBAbGysMWnSJOOOO+4wTCaT0aRJE2P27NnGxYsXHRnGYuPGjQaQ4dO/f3/DMAwjNTXVGD9+vFGmTBnDz8/PaN68ufHLL79YjdGiRQvL8dcsXrzYuOuuu4x8+fIZ1atXNyIiIhyqKz4+3gCM+Pj4WzovEXGcl5dhpEWItE8FjhgHqWYYYJyklFGHH6322/qIiPs58js0y88JCQ0NZePGjZQsWZJ+/foxcOBA7rrrLpeFI3fSc0JEslf6deN38zvrCaM8xzlCRUKJ5jDVMh1DMyAinsGR36FZvhxToEABIiIi6NChA97e3rddpIgIZAwgDdjNGtpSgjP8zt2EsZ7jlM90DAUQkZwpyyFk+fLlrqxDRPKg9AEkhO9YRmf8ucgPNKQdqzlDiUzHUAARyblu6+4YEZFblT6AdCaKNbTFn4tsoBWt+FYBRCSXUwgRkWy1bVvGADKAOUTQHT+SiaAb7VnFRfwzHUcBRCTnu+VbdEVEHGXrwcXP8S7vMgqAWQzkSWZivslfTQogIrmDZkJEJFtkDCAG/2OsJYC8xWge5/NMA0i+fAogIrlJlmZCHFmU2qlTp1suRkRyp/QBxAszHzGUIcwE4CWmMJUXyew9MKdOQcmSLixSRLJdlkJIly5drLZNJhM3Pl7kxpfDmc1m51QmIrlC+gCSj2Tm0Y+HWUQqJp7iEz7lyUzH0OyHSO6Upcsxqampls/69eupU6cOa9as4fz588THx7N69Wrq1avH2huftywieV76AFKQSyyjMw+ziGTy0ZuFCiAieZjDC1NHjBjBjBkzaNq0qaUtPDycggULMnjwYA4cOODUAkUkZ0ofQIpwjpV0oAk7uERBuhHJesIzHUMBRCR3cziE/PXXXwQGBmZoDwwM5MiRI86oSURyuPQBpAxxrCOce/mFcxShPavYSeZvtlYAEcn9HL47pmHDhowYMYK4uDhL28mTJxk1ahT33XefU4sTkZwnfQCpzN9soyn38gtxlKE5WzINIMWLK4CI5BUOh5DZs2dz6tQpKlasSNWqValatSoVKlQgLi6OWbNmuaJGEckh0geQe/iFbTSlCn/zF3fQhO38Si27/efPh9OnXVykiHgMhy/HVK1alZ9//pno6Gj++OMPDMOgRo0atG7d2uouGRHJW9L/8X+AnaymHUU5zy/cQxjrOUlZu/1TUkDvxhTJW0yGcesTn4mJifj5+eW68OHIa4hF8rrDh6FaNeu2UNazlK4U4jI7aER7VnGeonbH0OUXkdzDkd+hDl+OSU1NZfLkyZQrV47ChQsTExMDwLhx43Q5RiSP8fLKGEB6sJiVdKAQl1lHGKFEK4CIiE0Oh5D//e9/zJ07lzfffBNfX19Le61atfj888+dWpyIeC6TKWOAeJzPWEQvfLnKInrSkRVcppDdMRRARPI2h0PIvHnz+PTTT3nkkUfwvuEC7r333ssff/zh1OJExDPZugL7AlP5jMF4YTCDJ+nDAq7im/HA/6cAIiIOh5Djx49TtWrVDO2pqalcvXrVKUWJiOey9SK6qbzAVF4C4DVe5ik+IRX7q0wVQEQEbiGE1KxZk61bt2ZoX7x4MXXr1nVKUSLimdIHEG9S+JzHeYG3ABjF27zCa2T2IjoFEBG5xuFbdMePH0/fvn05fvw4qampREZGcvDgQebNm8fKlStdUaOIeID0AcSXJBbQh+5EYsaLJ/iMOQzMdAwFEBG5kcMzIR07dmTRokWsXr0ak8nEq6++yoEDB1ixYgWhoaGuqFFE3Gj//owBpDAXWEV7uhNJEr48xGIFEBFxmEMzISkpKbz22msMHDiQzZs3u6omEfEQthagFuMMq2nH/fzARQrRmWV8R6tMx1EAERFbHJoJ8fHx4a233sJsNruqHhHxELYCSBDH2UJz7ucHzlCMB/lOAUREbpnDl2Nat27Npk2bXFCKiHgKWwGkKofYThNq8jvHKEcztrIb+y+t/OcfBRARyZzDC1Pbtm3LmDFj+PXXX6lfvz6FClk/iKhTp05OK05Esp+tAFKb/awjnNKc4k+qEUo0sVS0O4bCh4hkhcPvjvHysj95YjKZcsWlGr07RvKi2FioaCNXNGUrK+hIEeLZRx3asJZTlLY7jgKISN7myO9Qh2dCUlNTb7kwEfFM+fKlvcU2vXasYgk9KEAiW2hGR1aQQKDdcRRARMQRDq8JuVFiYqKz6hARNzGZbAeQ3iwgii4UIJGVtKcNaxVARMSpHA4hZrPZ6i26f//9N6C36IrkRLbWfwA8zUfM51HykcJX9KErS7lCQbvjKICIyK1wOIS89tpreouuSC5gO4AYvMJkPmIYXhh8yDD68iUp5LM5Rr58CiAicuv0Fl2RPMhWADGRyns8x2ReBWAC43mWDzDs/DVx6hQkJ7uyShHJ7RxemKq36IrkbLYCiDcpzGIQ/ZkHwLO8z4c8a3cMzX6IiDPoLboieYitAJKfK0TQnf7MIwVv+jJPAUREsoXeoiuSR9gKIP4ksJxOtGQzifjxEItZSUe7YyiAiIgz6S26InmArQBSgv/YSAgt2UwC/oSzzm4AKVpUAUREnM/hJ6bmBXpiquQmtgJIMLGsJ4zqHOQUJWnDWvZRz2b/8+ch0P7jQURErLj0iakiknPYCiB38QfRhBLMMWIJJpRo/uQum/31vygi4kpZCiFFixbFZO+pRumcPXv2tgoSEeew9Ue2HntZSxtKcpoDVCeM9Rwj2GZ/BRARcbUshZBp06ZZvj5z5gz/+9//CA8Pp1GjRgDs3LmTdevWMW7cOJcUKSKOsRVAWrCJ5XQigAvspgFtWcMZStjsrwAiItnB4TUh3bt3JyQkhGHDhlm1T58+nQ0bNhAVFeXM+txCa0IkJ7MVQDqxjEX0Ij9JfEcInVnGRfxt9lcAEZHb4cjvUIfvjlm3bh1t2rTJ0B4eHs6GDRscHU5EnMhWAOnHF0TQnfwkEUVn2rFaAUREPILDIaR48eIsXbo0Q3tUVBTFixd3SlEi4jhbAWQ40/iCAfhgZg4D6MESkshvs78CiIhkN4fvjpk4cSKDBg1i06ZNljUh33//PWvXrtUL7ETcwGwGnwx/kg0m8Srj+B8A7/Ico3nb7ntgFEBExB0cngkZMGAAO3bsoEiRIkRGRhIREUFgYCDbt29nwIABLihRROyJjMwYQEykMp1hlgAylv8xincUQETE4zg0E3L16lUGDx7MuHHj+Oqrr1xVk4hkwZdfQr9+1m0+XOUL+tOHhaRiYigfMYOn7I6hACIi7uTQTEi+fPlsrgdxpUqVKmEymTJ8hg4davP4TZs22Tz+jz/+yNa6RVwpODhjACnAZaLoQh8WchUf+rBAAUREPJrDa0K6du1KVFQUI0eOdEU9GezevRuz2WzZ/vXXXwkNDeWhhx7KtN/Bgwetbg0qWbKky2oUyU62FqAGcp4VdKQZ27hMAboTwVra2h1DAUREPIHDIaRq1apMnjyZHTt2UL9+fQoVKmS1/9ln7b8C/FakDw9vvPEGVapUoUWLFpn2K1WqFEWKFHFqLSLuZiuAlOYka2lDHX7iPIG0ZxU7aGJ3DAUQEfEUDoeQzz//nCJFirB371727t1rtc9kMjk9hNwoOTmZ+fPnM3LkyJs+Rr5u3bokJiZSo0YNXnnlFUJCQuwem5SURFJSkmU7ISHBaTWLOMOVK1CwYMb2SsQQTShV+YuTlCacdfxMbbvjKICIiCdxOITExMS4oo4siYqK4vz585nehVO2bFk+/fRT6tevT1JSEl9++SWtWrVi06ZNNG/e3GafKVOmMHHiRBdVLXJ72rWDNWsyttfgN9YTRjlOEEMlQonmL6raHUcBREQ8jcOPbb/m9OnTmEymbH1AWXh4OL6+vqxYscKhfh07dsRkMrF8+XKb+23NhAQHB+ux7eJ2fn6QnJyx/T52sZp2FOcsv1KTcNZxgnI2x/DySnuWiIhIdnDZY9vPnz/P0KFDKVGiBKVLl6ZUqVKUKFGCYcOGcf78+dup+ab++ecfNmzYwOOPP+5w3wceeIBDhw7Z3e/n50dAQIDVR8TdTCbbAaQVG/iWVhTnLN9zP83ZYjeAFCyoACIinivLl2POnj1Lo0aNOH78OI888gh33303hmFw4MAB5s6dy7fffsuOHTsoWrSoSwqdM2cOpUqVon379g733bdvH2XLlnVBVSKuYW/JUzciWEAf/EhmPaF0I5JLFLZ5bFwclCnjwiJFRG5TlkPIpEmT8PX15a+//qJ06dIZ9oWFhTFp0iTee+89pxeZmprKnDlz6N+/Pz7pHg85ZswYjh8/zrx58wCYNm0alSpVombNmpaFrBEREURERDi9LhFXsBdABvE5M3kSb1JZTA8eZT7J+Nk8Vus/RCQnyPLlmKioKN5+++0MAQSgTJkyvPnmmy57kNmGDRuIjY1l4MCBGfbFxcURGxtr2U5OTmb06NHce++9NGvWjG3btrFq1Sq6devmktpEnMnPdqbged7kc57Am1Q+43Ee5msFEBHJ8bK8MNXPz4+//vqL8uXL29x/7NgxqlatSmJiolMLdAdHFtWIOMt//0GpUulbDaYwhpeYCsAbvMgYpgC2p0sUQETE3VyyMLVEiRIcOXLE7v6YmJhsvVNGJLdJH0C8MDOTJy0B5AWmMoY3UAARkdwiyyGkTZs2jB07lmQby/WTkpIYN24cbdq0cWpxInlBbGzGdSC+JLGQ3gzmM8x48Tif8RYv2OxfvboCiIjkTFm+HHPs2DEaNGiAn58fQ4cOpXr16gD8/vvvfPzxxyQlJbFnzx6Cg4NdWnB20OUYyS4+PhlvoS3ERSLpRhjRJJOPPiwggh42+1+4AIVt3xwjIuIWjvwOzfLdMeXLl2fnzp08/fTTjBkzhmvZxWQyERoayvTp03NFABHJLrbuginKWVbRnkZ8z0UK0ZWlbCDUZn/NfohITufQY9srV67MmjVrOHfunOXhX1WrVqVYsWIuKU4kt7IVQMpygnWEU4tfOUtR2rKGH7jfZn8FEBHJDRx+dwxA0aJFue+++5xdi0ieYCuAVOEw6wnjDmI4ThBhrOd3atrsrwAiIrmFQ49tF5FbFx9vO4DU4me20ZQ7iOEwVWjKNgUQEckTFEJEskGlSlCkSMb2xmxnC80pw7/8xL00ZRtHqGxzjMuXXVqiiEi2u6XLMSKSdfYewx7OWiLpRkGusI0mdGAl8RSxeWznzlCggOtqFBFxB82EiLiQvQDSi69ZQUcKcoXVtCWM9ZkGkKgol5UoIuI2mgkRcRF7AeRJZvAxT+OFwQJ6M4C5XMXX5rGXL2sGRERyL82EiLiA7QBiMIbXmcFTeGHwEU/zKPPtBhDDUAARkdxNIUTEyWwFEBOpvM1oXmcsAJN5hWFMx7DzR1B3wYhIXqDLMSJOZCuAeJPCZzzBY8wFYATv8T4jbPb38YGrV11Xn4iIJ1EIEXESWwHEj0QW0puuRJGCN4OYxTz62+xfsCBcuuTiIkVEPIgux4jcJrPZdgApzAVW046uRJGIH92JsBtAKldWABGRvEchROQ2fPZZ2iWU9Ipzmu94kAfZyAUK05Y1LKezzTHOn4e//3ZtnSIinkiXY0RuUb58kJKSsb08R1lPGHfzB/9RgrasYS8NbI6hBagikpcphIjcAnvPAKnGn0QTSkViOUp5QonmINVtHqsAIiJ5nS7HiDjIXgCpy49soykVieUgd9KE7QogIiKZUAgRySJ7C1ABmrOZTbSkFP+xl3o0YytHqWDzWAUQEZE0CiEiWRAZaXsBKkAHVrCWNgRwgU20IISN/EepDMf5+CiAiIjcSCFE5CYiI6F7d9v7HmE+S+lKARJZTkfasoYLBNg8Vg8hExGxphAikgmz2X4AeYYPmE9ffDAzj750J4JEbL/sRTMgIiIZKYSIZML2JRiD8UzgA4YDMI3hDGAuKeTLcGS5cgogIiL26BZdETvsvYhuGiN4lg8BGMck/scrQMaDz5+HwEDX1igikpMphIjYYCuA+HCVOTzGo3wFwFCm8zFDbfbX7IeIyM0phIikYyuA5OcKi3mIDqziKj705wsW0sdmfwUQEZGsUQgRuYGtABJAPCvoSHO2coX89GAJq2mf4bgiReDcOdfXKCKSW2hhqsj/sxVASvEvm2hJc7YSTwBhrLcZQOrXVwAREXGUZkJEsB1AKvAP0YRyJ4f4l1K0YS37qZvhuAsXoHDhbChSRCSXUQiRPM9WALmb31lPGOU5zhEqEko0h6mW4bjz5xVARERulS7HSJ5mK4A0YDdbaE55jvMbNWjKNpsBpHJl3YIrInI7FEIkz7IVQB7kW77jQUpwhl3cR3O2cJzyGY7z8oK//86GIkVEcjGFEMmTKth4wW0XlrKadvhzkQ20ojUbOEvxDMfly5f2OHcREbk9CiGS53zxBRw9at32GLNZQg/8SCaCbrRnFRfxz9C3Zk1ITs6mQkVEcjmFEMlTXngBBgywbhvJO8xmEN6kMouB9GIRyfhl6Js/P/z6a/bUKSKSFyiESJ7x5Zfw1ls3thj8j7G8w2gA3mI0j/M5Zhs3jfn4wJUr2VOniEheoVt0JU9o0AD27r2+7YWZjxjKEGYC8BJTmMqL2HoRXblycOxYNhUqIpKHKIRIrle6NJw6dX07H8nMox8Ps4hUTAxhBp8x2Gbf4sUVQEREXEUhRHI1X1+4evX6dkEuEUF32rCOZPLxKPNZTE+bfU0mOH06mwoVEcmDFEIkVzKb09Zx3KgI51hFexqzk0sUpBuRrCfc7hiJiS4uUkQkj9PCVMl1IiMzBpAyxLGZFjRmJ+coQms2ZBpAnn8+bRZFRERcRzMhkqtERkL37tZtlfmbaEKpwt/EUYYw1vMrteyO8fzz8OabLi5UREQUQiT3SE7OGEDu4RfWEU4QcfzFHYQSTQx32B3j8mUoUMDFhYqICKDLMZJLLFwIfumeL/YAO9lCc4KI4xfuoSnbMg0gEREKICIi2UkzIZLj3Xcf7N5t3RbKepbSlUJcZgeNaM8qzlPU7hgREdCtm4sLFRERKx49EzJhwgRMJpPVp0yZMpn22bx5M/Xr1yd//vzccccdzJgxI5uqFXfo3DljAOnBYlbSgUJcZi3hhBKdaQBJSVEAERFxB48OIQA1a9YkLi7O8vnll1/sHhsTE0O7du1o1qwZ+/bt4+WXX+bZZ58lIiIiGyuW7HLlCixfbt32BJ+yiF74cpWv6UUnlnOZQjb7e3mBYYC3dzYUKyIiGXj85RgfH5+bzn5cM2PGDCpUqMC0adMAuPvuu9mzZw9vv/023dOvWJQcLTkZCha8scXgRabyBmMAmMGTDOUjUrGdMNq0gTVrXF+niIjY5/EzIYcOHSIoKIjKlSvz8MMP8/fff9s9dufOnYSFhVm1hYeHs2fPHq7e+NjMdJKSkkhISLD6iOd67rn0i1AN3uQFSwB5jZd5ik/sBpB58xRAREQ8gUeHkPvvv5958+axbt06PvvsM06ePEnjxo05c+aMzeNPnjxJ6dKlrdpKly5NSkoKpzN5/vaUKVMIDAy0fIKDg516HuI8d9wB/z/RBYA3KXzO4zzP2wCM4m1e4TVsvYgOoGNH6NvX9XWKiMjNeXQIadu2Ld27d6dWrVq0bt2aVatWAfDFF1/Y7WMyWf/yMQzDZvuNxowZQ3x8vOVz9OhRJ1QvzhYQADEx17d9SWIRvRjEbMx4MZBZvMsou/0bNsy4hkRERNzH49eE3KhQoULUqlWLQ4cO2dxfpkwZTp48adV26tQpfHx8KF68uN1x/fz88Ev/kAnxKCVLwoUL17cLc4GldKU135KELw/zNVF0tdt/wQLo3TsbChURkSzLUSEkKSmJAwcO0KxZM5v7GzVqxIoVK6za1q9fT4MGDciXL192lCguUKGC9dtsi3GG1bTjfn7gAoXpQhTf0cpu/5QU3QEjIuKJPPpyzOjRo9m8eTMxMTHs2rWLHj16kJCQQP/+/YG0yyj9+vWzHD9kyBD++ecfRo4cyYEDB5g9ezazZs1i9OjR7joFuU0FCsCNV8eCOM4WmnM/P3Ca4jzId5kGEN2CKyLiuTx6JuTYsWP07t2b06dPU7JkSR544AG+//57KlasCEBcXByxsbGW4ytXrszq1at57rnn+OijjwgKCuKDDz7Q7bk5lL8/JCZe367KIaIJpRL/cIxyhLGeA9Sw2z8pKRuKFBGRW2Yyrq3cFIuEhAQCAwOJj48nICDA3eXkScOGwUcfXd+uzX7WEU5pTvEn1Qglmlgq2u2vN+GKiLiHI79DPfpyjORNycnWAaQpW9lMC0pzin3UoRlbFUBERHIBj74cI3lT3brXv27HKpbQgwIksoVmdGQFCQTa7FekCPz7L/j6Zk+dIiJyezQTIh5l2DD4/fe0r3uzgCi6UIBEVtKeNqy1G0DatoVz5xRARERyEs2EiEdIToayZeHs2bTtp/mID3kGLwzm8wiPMYcUbN9mXa8erF6djcWKiIhTaCZE3G7UqLR3waQFEINxTOIjhuGFwQc8Qz/m2Q0gDRrA3r3ZWq6IiDiJQoi4VcOG8O67aV+bSGUaI5jEeAAmMJ7hvI9h5z/TMWNg9+7sqlRERJxNl2PEberXhx9/TPvah6vMYhD9+BKAZ3mfD3nWbt8CBWDy5OyoUkREXEUhRNyiQ4frASQ/V1hELzqxghS8eYw5zCfzV93OnasnoYqI5HQKIZLt2re/vpDUnwSW04mWbCYRPx5iMSvpmGn/Dh2gZ89sKFRERFxKIUSyTfo7YErwH2tpQ31+JJ4AOrGcLbTIdIw77oB07ygUEZEcSgtTJVs8//yNd8BAMLFspRn1+ZFTlCSEjTcNIJUrw19/ZUOxIiKSLRRCxOW6dIG3376+fRd/sJ0mVOcg/1CBpmxjH/UyHWP4cPj7b9fWKSIi2UuXY8SlFi6EZcuub9dnD2toS0lOc4DqhLGeYwTb7R8UBDExehKqiEhupJkQcZlFi6BPn+vbLdnIRkIoyWl204BmbM00gDz7LBw/rgAiIpJbKYSI05nN8NBD8PDD19s6sYw1tMWfi3xHCA/yHWcoYXeMESPg/fddX6uIiLiPQog4VWQkFCoES5Zcb+vHF0TQnfwkEUVn2rGai/jbHaNTJ3jvvWwoVkRE3EohRJzCbIYJE6B7d0hKut4+nGl8wQB8MDOHAfRgCUnktzvOqFHWa0hERCT30sJUuW2RkfDEE9dvv01jMIlXGcf/AHiX5xjN23bfA1O0KJw8qfUfIiJ5iWZC5LZERqbNftwYQEykMp1hlgDyMq8xinfsBpBu3dL6K4CIiOQtmgmRW2Y2p93BcqN8JPMF/enN16RiYigfMYOn7I5RtCh8842LCxUREY+kECK3bOvWtFtorynAZZbQg3as4So+9OVLFvGw/QGAzz/Xi+hERPIqhRC5JWYzvPji9e1AzrOSDjRlO5cpQHciWEtbu/3z54evvkq7FCMiInmT1oSIw5YsgQIF4Icf0rZLc5JNtKQp2zlPIKFE2w0gJhOMGwcXLyqAiIjkdZoJEYe88AK89db17UrEEE0oVfmLk5QmnHX8TG2bfR94ALZt0+UXERFJo5kQybLFi60DSA1+YxtNqcpfxFCJpmyzG0A6doSdOxVARETkOoUQyRKzGR5//Pr2fexiC80pxwl+pSZN2M5fVLXZ96GHYPnybCpURERyDIUQyZJHHoGEhLSvWxPNt7SiOGfZyQM0ZwtxBNnsFxSU9iZdERGR9BRC5KYWL057Iy5Ad5awivYU5hLrCSWUaM5RzG7fDz/UJRgREbFNIUQydeNlmEF8ziJ64ctVFtODjqzgEoVt9vP3h4gI3QEjIiL26e4YydRrr6VdhnmeN3mTtAeDfMbjDGEGqdie4mjcGLZs0QyIiIhkTjMhYpfZDO9PM5jCS5YA8gYvMphP7QaQUaNg+3YFEBERuTnNhIhdWzeZmXLuKQbzGQAvMJW3eMHmsb6+cP582kPMREREskIhRGxLSqLIU30ZzGLMePEkM5nF43YP/+orBRAREXGMQohkYI6/yPlW3ahzKJokfOnDAiLpbvf4Xr2gR49sLFBERHIFrQkRKyu+OMtPpVpTfG80FylEe1ZlGkD8/dNmQURERBylECJA2iLUd0efoPKA5tRL3sVZitKKb/mW1pn2GzRIi1BFROTW6HJMHmY2w9atEBUFm2cdJvJiKJU5wnGCCGM9v1PzpmN07uz6OkVEJHdSCMmDzOa053+8/z6cPQu1+Jn1hFGGfzlMFUKJ5giVbzpO8eLQrFk2FCwiIrmSQkgud222Iy4OSpVK+/qdd+DixbT9jdnOKtpThHj2U5s2rOVfymRp7Gef1aUYERG5dQohuVhkJAwfDseO2d4fzloi6UZBrrCNJnRgJfEUydLYAQEwdqzzahURkbxHC1NzIbMZJk2C7t3tB5BefM0KOlKQK6ymLWGsz3IAAZg1S7MgIiJyexRCcpnISKhYEcaPt3/MED5hAX3IRwoL6E0XorhCwSx/j+ef13NBRETk9ulyTC4SGZkWDgzD3hEGL/M6r/EKAB/xNM/wIUYWs2iJEvDxx/DQQ86pV0RE8jbNhOQSZnPa+g97AcREKu8wyhJAJvMKw5ie5QAycSKcPKkAIiIizqOZkFxi0yb76z+8SeEznuAx5gIwgvd4nxFZGjc4GKZNg27dnFGliIjIdQohOdCNt92WLQunT8OTT9o+1o9EFtKbrkSRgjeDmMU8+mc6fmAg9O8PXbumPQdEC1BFRMQVPDqETJkyhcjISP744w8KFChA48aNmTp1KnfddZfdPps2bSIkJCRD+4EDB6hevbory80WN7vt9kaFucAyOvMgG0nEj558wwo6ZTiuUKG0yyytW0O5cgoeIiKSPTw6hGzevJmhQ4fSsGFDUlJSGDt2LGFhYfz+++8UKlQo074HDx4kICDAsl2yZElXl+tyN194el0J/mM17WjIHhLwpxPL2UxLq2OKFUsLNGPHKnSIiEj28+gQsnbtWqvtOXPmUKpUKfbu3Uvz5s0z7VuqVCmKFCniwuqy180Wnt6oPEdZTxh38wf/UYI2rOVH6jN+fNosx6lTaZdxNOMhIiLu5NEhJL34+HgAihUrdtNj69atS2JiIjVq1OCVV16xeYnmmqSkJJKSkizbCQkJt1+sk23dmrVLMHdykGhCqcBRjlKeUKI5Xbw6EZ9qcamIiHiWHHOLrmEYjBw5kqZNm3LPPffYPa5s2bJ8+umnREREEBkZyV133UWrVq3YsmWL3T5TpkwhMDDQ8gkODnbFKdyWuLibH1OXH9lKMypwlIPcSRO2c5DqLFqkACIiIp7HZBhZmeB3v6FDh7Jq1Sq2bdtG+fLlHerbsWNHTCYTy5cvt7nf1kxIcHAw8fHxVutK3GnTJshkMofmbGYFHQngAnupR1vWcNpUivLlISZGl11ERCR7JCQkEBgYmKXfoTliJuSZZ55h+fLlbNy40eEAAvDAAw9w6NAhu/v9/PwICAiw+niaZs2gfHkwmTLu68AK1tKGAC6wiRaEsJHTplJA2jM+FEBERMQTeXQIMQyDYcOGERkZyXfffUflypVvaZx9+/ZRtmxZJ1eXvby94f33076+MYg8wnyW0pUCJLKMTrRlDRcIoHx5WLJEl2FERMRzefTC1KFDh7JgwQKWLVuGv78/J0+eBCAwMJACBQoAMGbMGI4fP868efMAmDZtGpUqVaJmzZokJyczf/58IiIiiIiIcNt5OEu3bmnB4tpzQp7hAz5gOABHmvejyKuzmH3KR3e+iIhIjuDRIeSTTz4BoGXLllbtc+bMYcCAAQDExcURGxtr2ZecnMzo0aM5fvw4BQoUoGbNmqxatYp27dplV9lOkf6pqNdCRbdu0LmTwdFBE6g0bxIAqc8Op9J771LJy6MntkRERKzkmIWp2cmRRTWuYOupqOXLp12O6dYlNW3n9OlpOyZNgldesb1YREREJJs58jvUo2dC8iJ7T0U9fhwe7n6Vw80fo8KWr9Iap0+HoUOzv0gREREnUAjxIJk9FdXPuMJiHqLCllUYPj6YvvgC+vTJ/iJFREScRIsIPIi9p6IGEM86wunAKq6Qn18mRSmAiIhIjqcQ4kFsPRW1FP+yiZY0ZyvxBBDGen6r1D77ixMREXEyhRAPkv5RJhU5wlaaUZf9/EspWrCZbTTLcJyIiEhOpBDiQW58Kurd/M42mnInhzhCRZqyjZ9NdQgOTjtOREQkp1MI8SDXnora0PiBrTSjPMf5jRo0YTt/maoBegy7iIjkHgohHqZb4Ldsz/8gxTnLLu6jOVs4QTk9hl1ERHId3aLrSZYuhYcfxic5GePBViSPWsr0eH89hl1ERHIlhRBPMXs2PPEEpKZCt26YFiygmZ+fu6sSERFxGV2O8QTvvAODBqUFkEGDYNEiUAAREZFcTiHEnQwDxo6F0aPTtp9/Hj77DHw0QSUiIrmfftu5i9mc9t6XmTPTtt94A1580b01iYiIZCOFEHdIToa+feGbb9IeCjJjBgwe7O6qREREspVCSHa7dAm6d4d16yBfPpg/H3r2dHdVIiIi2U4hJDudOwft28POnVCwIERGQni4u6sSERFxC4WQ7BIXlxY4fvkFihSB1auhUSN3VyUiIuI2CiHZwTCgY8e0AFK2bNqlmFq13F2ViIiIW+kW3exgMqW99OWee2DbNgUQERERNBOSfZo2hf379ex1ERGR/6eZkOykACIiImKhECIiIiJuoRAiIiIibqEQIiIiIm6hECIiIiJuoRAiIiIibqEQIiIiIm6hECIiIiJuoRAiIiIibqEQIiIiIm6hECIiIiJuoRAiIiIibqEQIiIiIm6hECIiIiJuoRAiIiIibqEQIiIiIm6hECIiIiJuoRAiIiIibqEQIiIiIm6hECIiIiJuoRAiIiIibuHj7gLyArMZtm6FuDgoWxaaNQNvb3dXJSIi4l4KIS4WGQnDh8OxY9fbypeH99+Hbt3cV5eIiIi76XKMC0VGQo8e1gEE4PjxtPbISPfUJSIi4gkUQlzEbE6bATGMjPuutY0YkXaciIhIXqQQ4iJbt2acAbmRYcDRo2nHiYiI5EUKIS4SF+fc40RERHKbHBFCPv74YypXrkz+/PmpX78+W28yfbB582bq169P/vz5ueOOO5gxY0Y2VXpd2bLOPU5ERCS38fgQsmjRIkaMGMHYsWPZt28fzZo1o23btsTGxto8PiYmhnbt2tGsWTP27dvHyy+/zLPPPktERES21t2sWdpdMCaT7f0mEwQHpx0nIiKSF5kMw9bSSc9x//33U69ePT755BNL2913302XLl2YMmVKhuNffPFFli9fzoEDByxtQ4YM4aeffmLnzp02v0dSUhJJSUmW7YSEBIKDg4mPjycgIOCWa792dwxYL1C9FkyWLNFtuiIikrskJCQQGBiYpd+hHj0TkpyczN69ewkLC7NqDwsLY8eOHTb77Ny5M8Px4eHh7Nmzh6tXr9rsM2XKFAIDAy2f4OBgp9TfrVta0ChXzrq9fHkFEBEREY8OIadPn8ZsNlO6dGmr9tKlS3Py5EmbfU6ePGnz+JSUFE6fPm2zz5gxY4iPj7d8jh496pwTIC1oHDkCGzfCggVp/4yJUQARERHJEU9MNaVbWGEYRoa2mx1vq/0aPz8//Pz8brNK+7y9oWVLlw0vIiKSI3n0TEiJEiXw9vbOMOtx6tSpDLMd15QpU8bm8T4+PhQvXtxltYqIiIhjPDqE+Pr6Ur9+faKjo63ao6Ojady4sc0+jRo1ynD8+vXradCgAfny5XNZrSIiIuIYjw4hACNHjuTzzz9n9uzZHDhwgOeee47Y2FiGDBkCpK3n6Nevn+X4IUOG8M8//zBy5EgOHDjA7NmzmTVrFqNHj3bXKYiIiIgNHr8mpFevXpw5c4ZJkyYRFxfHPffcw+rVq6lYsSIAcXFxVs8MqVy5MqtXr+a5557jo48+IigoiA8++IDu3bu76xRERETEBo9/Tog7OHKPs4iIiFyXa54TIiIiIrmXQoiIiIi4hUKIiIiIuIVCiIiIiLiFQoiIiIi4hUKIiIiIuIVCiIiIiLiFQoiIiIi4hcc/MdUdrj2/LSEhwc2ViIiI5CzXfndm5VmoCiE2XLhwAYDg4GA3VyIiIpIzXbhwgcDAwEyP0WPbbUhNTeXEiRP4+/tjMpkyPTYhIYHg4GCOHj2a6x7xnpvPDXL3+eXmc4PcfX65+dwgd59fbj43yPr5GYbBhQsXCAoKwssr81UfmgmxwcvLi/LlyzvUJyAgIFf+Rwe5+9wgd59fbj43yN3nl5vPDXL3+eXmc4Osnd/NZkCu0cJUERERcQuFEBEREXELhZDb5Ofnx/jx4/Hz83N3KU6Xm88Ncvf55eZzg9x9frn53CB3n19uPjdwzflpYaqIiIi4hWZCRERExC0UQkRERMQtFEJERETELRRCRERExC0UQlwgKSmJOnXqYDKZ2L9/v7vLcZpOnTpRoUIF8ufPT9myZenbty8nTpxwd1m37ciRIwwaNIjKlStToEABqlSpwvjx40lOTnZ3aU7z2muv0bhxYwoWLEiRIkXcXc5t+fjjj6lcuTL58+enfv36bN261d0lOcWWLVvo2LEjQUFBmEwmoqKi3F2S00yZMoWGDRvi7+9PqVKl6NKlCwcPHnR3WU7zySefcO+991oe4tWoUSPWrFnj7rJcYsqUKZhMJkaMGOGU8RRCXOCFF14gKCjI3WU4XUhICN988w0HDx4kIiKCv/76ix49eri7rNv2xx9/kJqaysyZM/ntt9947733mDFjBi+//LK7S3Oa5ORkHnroIZ566il3l3JbFi1axIgRIxg7diz79u2jWbNmtG3bltjYWHeXdtsuXbpE7dq1mT59urtLcbrNmzczdOhQvv/+e6Kjo0lJSSEsLIxLly65uzSnKF++PG+88QZ79uxhz549PPjgg3Tu3JnffvvN3aU51e7du/n000+59957nTeoIU61evVqo3r16sZvv/1mAMa+ffvcXZLLLFu2zDCZTEZycrK7S3G6N99806hcubK7y3C6OXPmGIGBge4u45bdd999xpAhQ6zaqlevbrz00ktuqsg1AGPp0qXuLsNlTp06ZQDG5s2b3V2KyxQtWtT4/PPP3V2G01y4cMGoVq2aER0dbbRo0cIYPny4U8bVTIgT/fvvvzzxxBN8+eWXFCxY0N3luNTZs2f56quvaNy4Mfny5XN3OU4XHx9PsWLF3F2G3CA5OZm9e/cSFhZm1R4WFsaOHTvcVJXcivj4eIBc+WfMbDbz9ddfc+nSJRo1auTucpxm6NChtG/fntatWzt1XIUQJzEMgwEDBjBkyBAaNGjg7nJc5sUXX6RQoUIUL16c2NhYli1b5u6SnO6vv/7iww8/ZMiQIe4uRW5w+vRpzGYzpUuXtmovXbo0J0+edFNV4ijDMBg5ciRNmzblnnvucXc5TvPLL79QuHBh/Pz8GDJkCEuXLqVGjRruLsspvv76a3788UemTJni9LEVQm5iwoQJmEymTD979uzhww8/JCEhgTFjxri7ZIdk9fyuef7559m3bx/r16/H29ubfv36YXjoQ3cdPTeAEydO0KZNGx566CEef/xxN1WeNbdyfrmByWSy2jYMI0ObeK5hw4bx888/s3DhQneX4lR33XUX+/fv5/vvv+epp56if//+/P777+4u67YdPXqU4cOHM3/+fPLnz+/08fXY9ps4ffo0p0+fzvSYSpUq8fDDD7NixQqrvwzNZjPe3t488sgjfPHFF64u9ZZk9fxs/cd37NgxgoOD2bFjh0dOOzp6bidOnCAkJIT777+fuXPn4uXl2Rn9Vv7dzZ07lxEjRnD+/HkXV+d8ycnJFCxYkMWLF9O1a1dL+/Dhw9m/fz+bN292Y3XOZTKZWLp0KV26dHF3KU71zDPPEBUVxZYtW6hcubK7y3Gp1q1bU6VKFWbOnOnuUm5LVFQUXbt2xdvb29JmNpsxmUx4eXmRlJRktc9RPs4oMjcrUaIEJUqUuOlxH3zwAf/73/8s2ydOnCA8PJxFixZx//33u7LE25LV87PlWn5NSkpyZklO48i5HT9+nJCQEOrXr8+cOXM8PoDA7f27y4l8fX2pX78+0dHRViEkOjqazp07u7EyuRnDMHjmmWdYunQpmzZtyvUBBNLO2VP/bnREq1at+OWXX6zaHnvsMapXr86LL754WwEEFEKcpkKFClbbhQsXBqBKlSqUL1/eHSU51Q8//MAPP/xA06ZNKVq0KH///TevvvoqVapU8chZEEecOHGCli1bUqFCBd5++23+++8/y74yZcq4sTLniY2N5ezZs8TGxmI2my3Pr6latarlv9WcYOTIkfTt25cGDRrQqFEjPv30U2JjY3PF+p2LFy9y+PBhy3ZMTAz79++nWLFiGf5+yWmGDh3KggULWLZsGf7+/pY1PIGBgRQoUMDN1d2+l19+mbZt2xIcHMyFCxf4+uuv2bRpE2vXrnV3abfN398/w9qda+sCnbKmxyn32EgGMTExueoW3Z9//tkICQkxihUrZvj5+RmVKlUyhgwZYhw7dszdpd22OXPmGIDNT27Rv39/m+e3ceNGd5fmsI8++sioWLGi4evra9SrVy/X3Oa5ceNGm/+O+vfv7+7Sbpu9P19z5sxxd2lOMXDgQMt/kyVLljRatWplrF+/3t1luYwzb9HVmhARERFxC8+/8C0iIiK5kkKIiIiIuIVCiIiIiLiFQoiIiIi4hUKIiIiIuIVCiIiIiLiFQoiIiIi4hUKIiIiIuIVCiEgOdeTIEUwmk+UR7DlFpUqVmDZtmtPGa9myJSNGjHDaeO5gMpmIiooCcu6/V5FboRAi4oFMJlOmnwEDBri7xJuaO3cuRYoUydC+e/duBg8enP0FeYAJEyZQp06dDO1xcXG0bds2+wsScTO9wE7EA8XFxVm+XrRoEa+++ioHDx60tBUoUIBz5865ozSr13jfipIlSzq5opwvt7woUcRRmgkR8UBlypSxfAIDAzGZTBnarvn7778JCQmhYMGC1K5dm507d1qNtWPHDpo3b06BAgUIDg7m2Wef5dKlS5b9586do1+/fhQtWpSCBQvStm1bDh06ZNl/bUZj5cqV1KhRAz8/P/755x+Sk5N54YUXKFeuHIUKFeL+++9n06ZNAGzatInHHnuM+Ph4y+zNhAkTgIyXY86fP8/gwYMpXbo0+fPn55577mHlypUAnDlzht69e1O+fHkKFixIrVq1WLhwocM/zzfeeIPSpUvj7+/PoEGDeOmll6xmJGxd0unSpYvVjNP8+fNp0KAB/v7+lClThj59+nDq1CnL/k2bNmEymfj2229p0KABBQsWpHHjxpbwOHfuXCZOnMhPP/1k+ZnMnTsXsL4cY8vvv/9Ou3btKFy4MKVLl6Zv376cPn3asn/JkiXUqlWLAgUKULx4cVq3bm3171jEUymEiORwY8eOZfTo0ezfv58777yT3r17k5KSAsAvv/xCeHg43bp14+eff2bRokVs27aNYcOGWfoPGDCAPXv2sHz5cnbu3IlhGLRr146rV69ajrl8+TJTpkzh888/57fffqNUqVI89thjbN++na+//pqff/6Zhx56iDZt2nDo0CEaN27MtGnTCAgIIC4ujri4OEaPHp2h9tTUVNq2bcuOHTuYP38+v//+O2+88Qbe3t4AJCYmUr9+fVauXMmvv/7K4MGD6du3L7t27cryz+ebb75h/PjxvPbaa+zZs4eyZcvy8ccfO/xzTk5OZvLkyfz0009ERUURExNj87LY2LFjeeedd9izZw8+Pj4MHDgQgF69ejFq1Chq1qxp+Zn06tXrpt83Li6OFi1aUKdOHfbs2cPatWv5999/6dmzp2V/7969GThwIAcOHGDTpk1069YNvZtUcgSnvItXRFxmzpw5RmBgYIb2mJgYAzA+//xzS9tvv/1mAMaBAwcMwzCMvn37GoMHD7bqt3XrVsPLy8u4cuWK8eeffxqAsX37dsv+06dPGwUKFDC++eYby/cHjP3791uOOXz4sGEymYzjx49bjd2qVStjzJgxmdZdsWJF47333jMMwzDWrVtneHl5GQcPHszyz6Ndu3bGqFGjLNs3e614o0aNjCFDhli13X///Ubt2rUzHaNz585G//797Y77ww8/GIBx4cIFwzAMY+PGjQZgbNiwwXLMqlWrDMC4cuWKYRiGMX78eKvvew1gLF261DCM6/9e9+3bZxiGYYwbN84ICwuzOv7o0aMGYBw8eNDYu3evARhHjhyxW6uIp9JMiEgOd++991q+Llu2LIDlMsHevXuZO3cuhQsXtnzCw8NJTU0lJiaGAwcO4OPjw/33328Zo3jx4tx1110cOHDA0ubr62v1fX788UcMw+DOO++0Gnvz5s389ddfWa59//79lC9fnjvvvNPmfrPZzGuvvca9995L8eLFKVy4MOvXryc2NjbL3+PAgQM0atTIqi39dlbs27ePzp07U7FiRfz9/WnZsiVAhloy+/dxK/bu3cvGjRutfs7Vq1cH4K+//qJ27dq0atWKWrVq8dBDD/HZZ5+5bb2QiKO0MFUkh8uXL5/la5PJBKRd5rj2zyeffJJnn302Q78KFSrw559/2hzTMAzLWJC2EPbG7dTUVLy9vdm7d6/l0sk1hQsXznLtBQoUyHT/O++8w3vvvce0adOoVasWhQoVYsSIESQnJ2f5e2SFl5dXhssXN16OunTpEmFhYYSFhTF//nxKlixJbGws4eHhGWrJ7N/HrUhNTaVjx45MnTo1w76yZcvi7e1NdHQ0O3bsYP369Xz44YeMHTuWXbt2Ubly5Vv+viLZQSFEJBerV68ev/32G1WrVrW5v0aNGqSkpLBr1y4aN24MpC0G/fPPP7n77rvtjlu3bl3MZjOnTp2iWbNmNo/x9fXFbDZnWt+9997LsWPH+PPPP23OhmzdupXOnTvz6KOPAmm/kA8dOpRpbendfffdfP/99/Tr18/S9v3331sdU7JkSas7ksxmM7/++ishISEA/PHHH5w+fZo33niD4OBgAPbs2ZPlGq7Jys8kvXr16hEREUGlSpXw8bH9V7bJZKJJkyY0adKEV199lYoVK7J06VJGjhzpcI0i2UmXY0RysRdffJGdO3cydOhQ9u/fz6FDh1i+fDnPPPMMANWqVaNz58488cQTbNu2jZ9++olHH32UcuXK0blzZ7vj3nnnnTzyyCP069ePyMhIYmJi2L17N1OnTmX16tVA2l0wFy9e5Ntvv+X06dNcvnw5wzgtWrSgefPmdO/enejoaGJiYlizZg1r164FoGrVqpb/yz9w4ABPPvkkJ0+edOhnMHz4cGbPns3s2bP5888/GT9+PL/99pvVMQ8++CCrVq1i1apV/PHHHzz99NOcP3/esr9ChQr4+vry4Ycf8vfff7N8+XImT57sUB3XfiYxMTHs37+f06dPk5SUdNM+Q4cO5ezZs/Tu3ZsffviBv//+m/Xr1zNw4EDMZjO7du3i9ddfZ8+ePcTGxhIZGcl///3nUFATcReFEJFc7N5772Xz5s0cOnSIZs2aUbduXcaNG2dZqwAwZ84c6tevT4cOHWjUqBGGYbB69Wqrywq2zJkzh379+jFq1CjuuusuOnXqxK5duywzBY0bN2bIkCH06tWLkiVL8uabb9ocJyIigoYNG9K7d29q1KjBCy+8YJktGDduHPXq1SM8PJyWLVtSpkwZunTp4tDPoFevXrz66qu8+OKL1K9fn3/++YennnrK6piBAwfSv39/+vXrR4sWLahcubJlFgTSZkrmzp3L4sWLqVGjBm+88QZvv/22Q3UAdO/enTZt2hASEkLJkiWzdLtxUFAQ27dvx2w2Ex4ezj333MPw4cMJDAzEy8uLgIAAtmzZQrt27bjzzjt55ZVXeOedd/TwM8kRTEb6C6EiIrnchAkTiIqK0qPRRdxMMyEiIiLiFgohIiIi4ha6HCMiIiJuoZkQERERcQuFEBEREXELhRARERFxC4UQERERcQuFEBEREXELhRARERFxC4UQERERcQuFEBEREXGL/wMHFgO2NrAD0QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 600x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Create the QQ plot\n",
"fig, ax = plt.subplots(figsize=(6, 6))\n",
"res = stats.probplot(gaussian_sample_means, plot=ax, fit=True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "8a195c31",
"metadata": {},
"source": [
"The resulting QQ plot yields an almost perfect straight line which further confirms that the sample means do follow a Gaussian distribution.\n",
"\n",
"Now, put everything together in an interactive widget to experiment with different values for $\\mu$, $\\sigma$ and `sample_size`. **To update the plots you will need to click the `Run Interact` button after changing the parameters**:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "b0f89d4d",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "bd21db5cbfa647a2b537e2b820257ce7",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(FloatSlider(value=10.0, continuous_update=False, description='mu', max=50.0, min=0.01, r…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"utils.gaussian_clt()"
]
},
{
"cell_type": "markdown",
"id": "3a77283f",
"metadata": {},
"source": [
"Even with very small values for `sample_size` the sample means follow a Gaussian distribution. This is actually one of the properties of the Gaussian distribution.\n",
"\n",
"Now test the theorem with other distributions!"
]
},
{
"cell_type": "markdown",
"id": "dfa5768e",
"metadata": {},
"source": [
"## Binomial Population\n",
"\n",
"Now try with a population distribution that is not Gaussian. One such distribution is the Binomial distribution which you already saw covered in the lectures. To generate data that follows this distribution you will need to define values for the parameters of `n` and `p`:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "ef8c99cb",
"metadata": {},
"outputs": [],
"source": [
"n = 5\n",
"p = 0.8\n",
"\n",
"binomial_population = np.random.binomial(n, p, 100_000)"
]
},
{
"cell_type": "markdown",
"id": "5c733da4",
"metadata": {},
"source": [
"The population has a total of 100'000 observations. You can visualize its histogram by running the next cell:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "7124a3db",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.histplot(binomial_population, stat=\"count\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "1935bef1",
"metadata": {},
"source": [
"The mean and standard deviation is not as straightforward as in the Gaussian case (since these parameters were needed to generate the data in that case). However you can easily compute those values by drawing them directly from the population:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "35e417f8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Gaussian population has mean: 4.0 and std: 0.9\n"
]
}
],
"source": [
"binomial_pop_mean = np.mean(binomial_population)\n",
"binomial_pop_std = np.std(binomial_population)\n",
"\n",
"print(f\"Gaussian population has mean: {binomial_pop_mean:.1f} and std: {binomial_pop_std:.1f}\")"
]
},
{
"cell_type": "markdown",
"id": "c515c113",
"metadata": {},
"source": [
"Once again, in real life you will not have access to the whole population so you need another method to compute this values. Actually the mean and standard deviation of binomal distributions are well defined and can be computed by using the following formulas:\n",
"\n",
"- $\\mu = np$\n",
"\n",
"\n",
"- $\\sigma = \\sqrt{np(1-p)}$"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "bfeb5534",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Gaussian population has mean: 4.0 and std: 0.9\n"
]
}
],
"source": [
"binomial_pop_mean = n * p\n",
"binomial_pop_std = np.sqrt(n * p * (1 - p))\n",
"\n",
"print(f\"Gaussian population has mean: {binomial_pop_mean:.1f} and std: {binomial_pop_std:.1f}\")"
]
},
{
"cell_type": "markdown",
"id": "36ec734e",
"metadata": {},
"source": [
"Now you have found these same values but without needing to sample the whole population. Nice!\n",
"\n",
"Before seeing the theorem for this case, you should know that there is a rule of thumb to know if the theorem will hold or not for the Binomial distribution case. This condition is the following:\n",
"\n",
"if $min(Np, N(1-p)) >= 5$ then CLT holds\n",
"\n",
"where $N = n*sample\\_size$\n",
"\n",
"However, it is important to note that this rule is only a rough guideline, and other factors such as the presence of outliers and the purpose of the analysis should also be taken into consideration when choosing an appropriate statistical method.\n",
"\n",
"Now check the theorem in action. Begin by using a small `sample_size`:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "5aca48fd",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The condition value is: 2.9. CLT should hold?: False\n"
]
}
],
"source": [
"sample_size = 3\n",
"N = n * sample_size\n",
"\n",
"condition_value = np.min([N * p, N * (1 - p)])\n",
"print(f\"The condition value is: {int(condition_value*10)/10:.1f}. CLT should hold?: {True if condition_value >= 5 else False}\")"
]
},
{
"cell_type": "markdown",
"id": "f446cc20",
"metadata": {},
"source": [
"Perform the sampling and compute the theoretical values for the mean and standard deviation of the sample means. Remember these latter two can be computed like so:\n",
"\n",
"- $\\mu_{\\bar{X}} = \\mu$\n",
"\n",
"\n",
"- $\\sigma_{\\bar{X}} = \\frac{\\sigma}{\\sqrt{sample\\_size}}$"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "43fbbd16",
"metadata": {},
"outputs": [],
"source": [
"# Compute sample means\n",
"binomial_sample_means = sample_means(binomial_population, sample_size=sample_size)\n",
"\n",
"# Compute estimated mu\n",
"mu_sample_means = n * p\n",
"\n",
"# Compute estimated sigma\n",
"sigma_sample_means = np.sqrt(n * p * (1 - p)) / np.sqrt(sample_size)"
]
},
{
"cell_type": "markdown",
"id": "26c71c78",
"metadata": {},
"source": [
"Visualize the KDE vs Gaussian curve plot and the QQ plot to see how well the theorem is holding:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "ced8cb91",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1000x400 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Create the plots\n",
"utils.plot_kde_and_qq(binomial_sample_means, mu_sample_means, sigma_sample_means)"
]
},
{
"cell_type": "markdown",
"id": "e292d0cc",
"metadata": {},
"source": [
"This doesn't look as good as with the Gaussian example. It looks that by using a small `sample_size` the sample means do not follow a Gaussian distribution.\n",
"\n",
"Try again but now increasing the size of each sample:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "a15d5126",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The condition value is: 29.9. CLT should hold?: True\n"
]
}
],
"source": [
"sample_size = 30\n",
"N = n * sample_size\n",
"\n",
"condition_value = np.min([N * p, N * (1 - p)])\n",
"print(f\"The condition value is: {int(condition_value*10)/10:.1f}. CLT should hold?: {True if condition_value >= 5 else False}\")"
]
},
{
"cell_type": "markdown",
"id": "055109cb",
"metadata": {},
"source": [
"According to the rule of thumb, the theorem should hold under these conditions. Run the next cell to check if this is true:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "8b81b942",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1000x400 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"binomial_sample_means = sample_means(binomial_population, sample_size=sample_size)\n",
"\n",
"# Compute estimated mu\n",
"mu_sample_means = n * p\n",
"\n",
"# Compute estimated sigma\n",
"sigma_sample_means = np.sqrt(n * p * (1 - p)) / np.sqrt(sample_size)\n",
"\n",
"# Create the plots\n",
"utils.plot_kde_and_qq(binomial_sample_means, mu_sample_means, sigma_sample_means)"
]
},
{
"cell_type": "markdown",
"id": "2a86335a",
"metadata": {},
"source": [
"This time everything seems to indicate that the theorem is holding nicely!\n",
"\n",
"As with the previous distribution, by running the next cell you will launch an interactive widget in which you can play around with different values of $n$, $p$ and $sample\\_size$. \n",
"\n",
"See if you can find anything interesting, for instance does the theorem seem to hold better when $p$ is close to 0.5?"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "c292889c",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "88811703a8564074bb79013edc04009e",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(IntSlider(value=2, continuous_update=False, description='n', max=50, min=2), FloatSlider…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"utils.binomial_clt()"
]
},
{
"cell_type": "markdown",
"id": "94932c33",
"metadata": {},
"source": [
"Keep on going with another distribution!"
]
},
{
"cell_type": "markdown",
"id": "bebe0789",
"metadata": {},
"source": [
"## Poisson Population\n",
"\n",
"Another popular distribution you might have heard of is the `poisson` distribution. It models the number of events occurring in a fixed interval of time or space, given the average rate of occurrence $\\mu$ of those events.\n",
"\n",
"Since you are already familiar with the process of checking the theorem for a distribution you will skip all intermediate steps and jump straight to playing with the interactive widget.\n",
"\n",
"The only thing to consider here is that the mean and standard deviation of this distribution can be computed like this:\n",
"\n",
"- $\\mu = \\mu$\n",
"\n",
"\n",
"- $\\sigma = \\sqrt{\\mu}$"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "ec6cf35c",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "4a30dd55816448769ea4b89b42543e20",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(FloatSlider(value=1.5, continuous_update=False, description='mu', max=5.0, min=0.01, rea…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"utils.poisson_clt()"
]
},
{
"cell_type": "markdown",
"id": "5ccdb748",
"metadata": {},
"source": [
"As expected, you should see that the bigger the `sample_size` the more closely the distribution of the sample means follows a Gaussian distribution."
]
},
{
"cell_type": "markdown",
"id": "6152877c",
"metadata": {},
"source": [
"## Cauchy Distributions\n",
"\n",
"The Cauchy distribution is not as well-known as the other ones seen throughout this lab. It has heavy tails, which means that the probability of observing extreme values is higher than in other distributions with similar spread. It also does not have a well-defined mean or variance, which makes it less suitable for many statistical applications.\n",
"\n",
"As a result of the properties of this distribution, the central limit theorem does not hold. Run the next cell to generate a population of 1000 points that distribute Cauchy:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "6b3b4880",
"metadata": {},
"outputs": [],
"source": [
"cauchy_population = np.random.standard_cauchy(1000)"
]
},
{
"cell_type": "markdown",
"id": "493653bc",
"metadata": {},
"source": [
"Now take a look at the histogram of this population:"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "fd66119d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.histplot(cauchy_population, stat=\"density\", label=\"hist\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "7818e127",
"metadata": {},
"source": [
"It is very difficult to even see the histogram due to the extreme values it has. Now compute the sample means with a `sample_size` of 30, which is usually a safe bet for the theorem to hold under other distributions:"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "b58257ca",
"metadata": {},
"outputs": [],
"source": [
"cauchy_sample_means = sample_means(cauchy_population, sample_size=30)"
]
},
{
"cell_type": "markdown",
"id": "d5477a70",
"metadata": {},
"source": [
"Since this distribution has an undefined mean and standard deviation and the histogram is very hard to interpret you will only create the QQ plot for the sample means:"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "ee14767a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 600x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Create the QQ plot\n",
"fig, ax = plt.subplots(figsize=(6, 6))\n",
"res = stats.probplot(cauchy_sample_means, plot=ax, fit=True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "02976c76",
"metadata": {},
"source": [
"As you can see, this is very different from a straight line which let's you know that the sample means do not distribute normally. But what if you used a much bigger `sample_size`?"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "87f1b975",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 600x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cauchy_sample_means = sample_means(cauchy_population, sample_size=100)\n",
"\n",
"# Create the QQ plot\n",
"fig, ax = plt.subplots(figsize=(6, 6))\n",
"res = stats.probplot(cauchy_sample_means, plot=ax, fit=True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "c1ebed71",
"metadata": {},
"source": [
"Even when using a `sample_size` of 100, which might be unrealistic in real-life scenarios you still don't achieve normality for the sample means. This is important because it is a fact that the central limit theorem does not hold for all distributions and that is a limitation to consider when applying it."
]
},
{
"cell_type": "markdown",
"id": "930df17b",
"metadata": {},
"source": [
"**Congratulations on finishing this lab!**"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
}
},
"nbformat": 4,
"nbformat_minor": 5
}