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.