Mathematical Statistics

Aim

The course gives an introduction to mathematical modelling of experiments where the outcome is influenced by random factors. It is directed towards topics required for application in computer engineering. By the end of the course, the student should

• understand basic concepts in probability theory
• be able to set up relevant probability models for random experiments
• apply the techniques in the course to analyse these models
• describe and use some basic Mrakov models and their application

Content

Sample space, events and probabilities. Elementary combinatorial probability. Conditional probability and independence. Discrete random variables and probability distributions, expectation and variance. Binomial, Poisson distributions etc. The Probability Generating Function. Continuous Random Variables. Uniform, Exponential and Normal Distributions. Functions of random variables. Moment Generating Function. Simulating a Random Variable. Sampling. The Law of Large Numbers. The Central Limit Theorem. Stochastic Processes: The Poisson Process, introduction to Markov chains.