Learning Outcomes:
A good understanding of multivariate probability distributions, including conditional and marginal distributions. An ability to calculate and understand covariance and correlation coefficients. A knowledge and appreciation of the central limit theorem. A good understanding of the theory of estimation, including various methods for estimating parameters either with point estimates or confidence interval estimates. An ability to formulate and test statistical hypotheses and statements. An understanding of the methodology of many commonly used statistical tests. A good understanding of the principles of statistical decision theory and of optimality of estimators.
Indicative Module Content:
Probability theory: Continuous bivariate and multivariate distributions. Covariance and correlation. Chebyshev inequality. Law of Large Numbers. Central Limit Theorem and applications.
Statistics: Theory of Estimation. Method of moments, and maximum likelihood. Point and interval estimation. Properties and optimality of estimators. Hypothesis Testing. Simple and Composite Hypotheses. Neyman-Pearson Lemma and applications. Likelihood ratio tests. Introduction to statistical decision theory.