Probability Theory
The mathematics beneath statistics.
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Continuous Distributions in Depth
Density functions, transformations of random variables, and moment generating functions.
Joint Distributions
Joint, marginal and conditional distributions; covariance and correlation.
Expectation and Limit Theorems
Laws of large numbers and the Central Limit Theorem, proved and applied.
Introduction to Stochastic Processes
Markov chains, transition matrices, and long-run behaviour.