# Mathematical Statistics: Course Outline (MAT 413)

Mathematical statistics is the application of mathematics to statistics, which was originally conceived as the science of the state. the collection and analysis of facts about a country: its economy, land, military, population, and so forth.

## Course Contents

• Interpretations of Probability, Experiments and events, Definition of probability, Finite sample spaces, Counting methods,
• The probability of a union of events, Independent events,
• Definition of conditional probability,
• Bayes theorem. Random variables, discrete distributions and continuous distributions,
• Probability function and probability density function,
• The distribution function, Bivariate distributions, Marginal distributions, Conditional distributions, Multivariate distributions,
• Functions of random variables, The expectation of a random variable, Properties of expectations,
• Variance. Moments,
• The mean and the median, Covariance and correlation,
• Conditional expectation,
• Moment Generating functions,
• Probability distribution functions,
• Binomial, Negative Binomial
• Poisson,
• Normal Distribution.