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Textbook: Introduction to Probability and Mathematical Statistics
Author: Lee J. Bain
ISBN: 9780534380205

Syllabus

Homework

Simulations

Test Resources

Classroom:

Cina 102, 1:00-1:50 MWThF

Prerequisites:

Chapters 1-8 of the textbook will be covered, although we will omit a substantial part of Chapters 7 and 8. Here are some of the basic topics:

(1) Basic probability: sample space, events, properties of probability, conditional probability, independence.

(2) Random variables and their distributions: discrete and continuous (and mixed) random variables, expected values, variance, moment generating functions.

(3) Special probability distributions: discrete distributions (Bernoulli, binomial, hyper- geometric, geometric, negative binomial, Poisson, discrete uniform), continuous distributions (uniform, gamma, exponential, normal).

(4) Joint distributions: multinomial distribution, joint and marginal densities, joint cumulative distributions, independent random variables, conditional distribution.

(5) Properties of random variables: means and variances of sums of random variables, covariance and correlation, conditional expectation, bivariate normals.

(6) Functions of random variables: distributions of functions of random variables (cumulative distribution function technique, the Jacobian method), distributions of sums (convolutions, the moment generating function method).

(7) Limiting distributions: the Central Limit Theorem and the Law of Large Numbers.

(8) Statistics and sampling distributions: the chi-square, t, F, and beta distributions.