Mathematical Statistics: Basic Course

<p>The course gives a proper introduction to probability and statistics based on a mathematical foundation.</p><p>The course is divided into two halves, the first covers probability theory and the second covers statistics. The course covers:</p> <p>Sample space, Events, Basic set theory, Axioms of probability. Conditional probability, Independent events. Stochastic variables in one and several dimensions. Expectation, variance, and covariance. Normal distribution, binomial distribution, Poisson distribution and other important distributions. Conditional distributions and conditional expectations. Sums and linear combination of random variables. The law of large numbers, the central limit theorem and the law of rare events (Poisson limit). Point estimates and their properties. Maximum likelihood, Least squares and plugin estimators. Principles of interval estimates and hypothesis testing. Non-parametric test. Methods for observed data from standard distribution such as normal distribution, Binomial, Poisson and related distribution. Approximation methods based on the normal and Poisson distribution. Correlation. Linear regression.</p>