Canonical syllabus units, structured theorems, lecture notes, and past examination problems.
Introduces random variables and distinguishes between discrete and continuous random variables
Covers distribution functions for discrete and continuous random variables and their properties
Covers the mode and median as measures associated with probability distributions
Covers expectation for discrete and continuous random variables and properties of expectation
Covers moments and the properties of variance
Covers moment generating functions and probability generating functions
Covers special discrete probability distributions including Bernoulli, binomial, and hypergeometric distributions
Covers the Poisson distribution and the approximation of binomial probabilities
Covers the normal distribution, its moments, and the computation of normal probabilities
Covers gamma, exponential, and beta distributions, including moments of gamma and beta random variables
Covers change of variable for discrete and continuous distributions and direct derivation of the density function for a continuous random variable