Random Variables and Expectation
Discrete and continuous random variables, PMF, PDF and CDF and their properties, normalising a density and reading probabilities, median and expectation, expectation of a function, variance and its shortcut, linearity of expectation with indicator variables (fixed points, coupon collector), the tail-sum formula, joint tables with marginals, conditionals and independence, covariance and correlation with the uncorrelated-but-dependent example, and two solved past questions on a randomly broken stick.
