Mathematical Statistics

Course content: Probability theory: Basic concepts (for example: sample space, probability, inclusion, intersection, union...)<br> Dependent and independent events. Conditional probabilities.<br> Combinatorics<br> Stochastic variables: discrete and continuous, one-dimensional and multi-dimensional. Expectation and variance.<br> Known distributions: uniform (discrete and continuous), binomial, geometric, exponential, normal, t-distribution<br> The central limit theorem and normal approximation<br> Statistical inference: Point estimates<br> The maximum likelihood method and the method of moments<br> Confidence intervals for expectations, variance and proportions<br> Hypothesis testing<br> Linear regression<br> Simple experimental design<br> Statistical computations with computer