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.