Probability Theory

A course on probability theory may include the following topics:

• Sample space and events

• Axioms of probability and basic theorem

• Permutations, combinations, and Stirling's formula

• Conditional probability

• Law of multiplication

• Law of total probability

• Bayes' formula

• Independence

• Random variables

• Distribution functions

• Discrete random variables

• Expectations of discrete random variables

• Variances and moments of discrete random variables

• Standardized random variables

• Bernoulli and binomial random variables

• Poisson random variables

• Probability density functions

• The density function of a random variable

• Expectations and variances

• Uniform, normal, and exponential random variables

• Gamma and beta distributions

• Bivariate and multivariate distributions

• Covariance and correlation

For more details, refer to the following book:

Ghahramani, S. (2015). Fundamentals of probability: with stochastic processes. CRC Press.