ASV Chapters 1 - Sample Spaces and Probabilities 2 - Conditional Probability and Independence 3 - Random Variables 4 - Approximations of the Binomial Distribution 5 - Transforms and Transformations 6 - Joint Distribution of Random Variables 7 - Sums and Symmetry 8 - Expectation and Variance in the Multivariate Setting 9 - Tail Bounds and Limit Theorems 10 - Conditional Distribution 11 - Appendix A, B, C, D, E, F

Y = Exam Score X = Hours / Day studying 100 low probability 90 80 70 60 low probability Conditional distribution (of Y , given that X = 1) high probability low probability Conditional expectation (of Y , given that X = 1)

X = Hours / Day studying Y = Exam Score 100 90 80 70 60

“Conditional pmf” of X, given that Y = y Def: “Conditional pmf” of X, given that Y = y

“Conditional pmf” of X, given that Y = y Def: “Conditional pmf” of X, given that Y = y Def: “Conditional expectation” of X, given that Y = y

“Conditional pmf” of X, given that Y = y Def: “Conditional pmf” of X, given that Y = y Def: “Conditional expectation” of X, given that Y = y