MAT 221E - Probability Theory

Course Objectives

This course aims to:

1. To provide the basic concepts of probability.
2. To set up probability models for a range of random phenomena, both discrete and continuous.
3. To develop critical thinking skills and abilities to apply calculus techniques (i.e., limits,
derivatives, integration, infinite series) to assess the probability of an event.

Course Description

This course is an introductory level probability class on introducing following concepts: sample space, probability measure on a sigma-algebra, Kolmogorov axioms, conditional probability, combinatorial methods, Bayes theorem. Random variables, discrete density functions, continuous density functions, functions of random variables, bivariate joint density functions, marginal and conditional density functions, independent random variables. Definition and properties of expectations. Chebyshev inequality. Moment generating functions. Special discrete and continuous distributions. Limit theorems, law of large numbers, central limit theorem. Slutsky's theorem.