Mathematical Statistics

Statistics is a science which deals with collection, tabulation , presentation, analysis, and interpretation of the data. Mathematical statistics is the study of statistics from a mathematical point of view, using the theory of probability and various branches of mathematics such as linear algebra and analysis. It mainly includes Basic probability theory, Random variables and probability distributions, Normal and associated distributions. It mainly deals with the basic concepts of statistical theory such as likelihood functions, sufficient statistics, and exponential family of distributions. In addition, it includes the concepts of point estimation, minimum variance unbiased estimate (MVUE), Cramer-Rao inequality, Maximum likelihood estimates and asymptotic theory.

In addition, mathematical statistics includes further distribution theory such as Multivariate distributions, Transformations, Moment Generating Functions (MGF) and inequalities, Some limit theorems, and further discrete distributions such as Negative binomial, Hypergeometric and Multinomial distributions. Some of the continuous distributions discussed with relevant derivations and such distributions are Gamma and Beta functions, Gamma distribution, and Beta distribution. The necessary theoretical concepts are discussed for the multivariate normal distribution, Chi-square, t, and F distribution, and Normal theory tests and confidence intervals.

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