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.
- 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
- Normal Distribution.