- Probability density and distribution functions.
- Random variables and vectors, expectation, moments.
- Joint and marginal distributions.
- Conditional distributions and expectations.
- Transformations of random variables.
- Moment generating functions.
- Independence, laws of large numbers, central limit theorems.
- Special distributions (e.g., binomial, Poisson, normal, t, F, etc.).
- Basic combinatorics.
References
- Chung, Elementary Probability Theory
- Woodroofe, Probability with Applications
- Arnold, Mathematical Statistics
- Casella and Berger, Statistical Inference