This course studies basic probability theory and various distributions. Properties of distributions are derived.
Mean, variance, covariance and correlation
Discrete distributions including binomial, negative binomial, hypergeometric, Poisson, etc
Continuous distributions including uniform, normal, gamma, exponential, t, χ2, F, etc
Moment generating functions
Distributions of functions of random variables
Central limit theorem
Bain, Lee J. and Engelhardt, Max (1992) Introduction to Probability and Mathematical
Statistics, 2nd edition. Duxbury
Casella, George and Berger, Roger, L.
(1990) Statistical Inference.