The mathematical statistics prerequisite should cover the following topics:

  • Combinatorics and basic set theory notation
  • Probability definitions and properties
  • Common discrete and continuous distributions
  • Bivariate distributions
  • Conditional probability
  • Random variables, expectation, variance
  • Univariate and bivariate transformations
  • Convergence of random variables: in probability, in distribution, almost sure
  • Central Limit Theorem, Laws of Large Numbers
  • Estimation: bias, MSE, consistency, sufficiency, maximum likelihood, method of moments, UMVUE, Rao-Blackwell Theorem, Fisher Information
  • Hypothesis testing: significance level and power, Neyman-Pearson  lemma, Likelihood ratio tests
  • Confidence Intervals: definitions, duality with hypothesis tests