MATH230, Probability II

Undergraduate course, Lancaster University, Department of Mathematics & Statistics, 2017

My role: Graduate Teaching Assistant

Main topics:

  • Review of basic probability.

  • Random variables and their probability distribution functions. Probability mass functions and probability density function. Quantiles.

  • Expectation and variance of random variables; linearity of expectation. Higher-order moments.

  • Binomial, Poisson, uniform, geometric exponential. Review from first year and then further properties of the Poisson and exponential.

  • The gamma, normal, beta and chi-squared, and their inter-relationships and justification as probability models. The Cauchy and Student-$t$.

  • Joint distribution of vector random variables; that is, systems of two or more random variables, marginal and conditional distributions. Expectations and variances of vector variables. Moment generating functions.

  • Properties of linear combinations of random variables.

  • Transformations of random variables: motivation, univariate and bivariate methods.

  • Limit theory: convergence of variables, laws of large numbers, Central Limit Theorem.

  • Multivariate normal distribution.