Description:
This course studies basic probability theory and various distributions. Properties of distributions are derived.
Topics:
Sample space
Conditional probability
Random variables
Expected values
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
Limiting distributions
References:
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.