Math 477 - Mathematical Theory of Probability
Description
Math 477 is a calculus-based course covering foundational topics in probability theory.
Topics covered
Topics usually covered in Math 477 include:
- Introduction to probability, axioms of probability
- Basic combinatorics for probability
- Inclusion-exclusion principle
- Conditional probability and independent events
- Random variables and distribution functions
- Expected value and variance/covariance
- Common discrete distributions
- Common continuous distributions
- Distributions of functions of random variables
- Jointly distributed and independently distributed random variables
- Marginal distributions
- Conditional distributions and conditional expected value
- Moment generating functions
- Markov and Chebyshev inequalities
- Central limit theorem
Note that the exact list of topics may vary by instructor and semester.
Resources
Textbook
The usual textbook for the class is A First Course in Probability (10th edition) by Sheldon Ross. Introduction to Probability (1st edition) by David Anderson, Timo Seppäläinen, and Benedek Valkó may also be used as a textbook in some iterations of the course.