MATH 5312

 

Description:

 

This course studies basic probability theory and various distributions. Properties of distributions are derived.

 

Topics:

 

Sample space

Conditional probability

Independence

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. Wadsworth