{"ex1": {"mean": 3.5, "var": 2.916}, "ex2": {"hist": "left"}, "ex4": {"mean": 5.0, "var": 2.5, "cov": 0.0}, "ex5": {"hist": "right"}, "ex6": {"max_sum": 6}, "ex7": {"hist": "left-center"}, "ex8": {"hist": "right-most"}, "ex9": {"mean": "increases", "var": "increases", "cov": "stays the same"}, "ex10": {"options": "changing the loaded side from 1 to 6 will yield a higher mean but the same variance"}, "ex11": {"options": "changing the direction of the inequality will change the sign of the covariance"}, "ex12": {"options": "yes, but only if the die is fair"}, "ex3": {"sum_2_8": 0.0, "sum_3_7": 0.0, "sum_4_6": 0.0, "sum_5": 0.125}}