**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, *χ ^{2}*,
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, 2^{nd} edition. Duxbury

Casella, George and Berger, Roger, L.
(1990) Statistical Inference.