CA251 - Mathematical Statistics I

Review of Probability and Random Variables

Probability

Probability measures. Axioms for probability. Conditional probability
and independence.

Random Variables and Random Vectors. 

Density and distribution functions. Joint density functions, marginal density functions, conditional densities. Mathematical  Expectations. Moments of random variables and pairs of random variables.
 
Functions of Random Variables

Discrete Random Variables

Probability Generating Functions with applications (sums and moments) to special distributions:
Binomial, Poisson, Geometric. 

Distributions of functions of random variables. 

Moment Generating Functions with applications (linear combinations and moments) to special distributions: Normal, Gamma, Exponential, Chi-square. 

Distribution of functions of several random variables. 

The bivariate Normal.
Derivations of the densities the t and F distributions.

The Central Limit Theorem

Statement of The Central Limit Theorem and its application.

Textbooks

Hoel, Paul, Introduction to Mathematical Statistics, Wiley. 1984

Hogg, R. V. & Craig, A. T. Introduction to Mathematical Statistics, MacMillan, 1978.

A recent (Jan 2006) text I found good (and ordered 3 copies for library) is

Wackerly, Denis D., Mendenhall, William III and Scheaffer, Richard L., Mathematical Statistics with Applications, 2002, Duxbury.