To introduce statistical distribution theory which forms the basis for all applications of statistics, and for further statistical theory.

After completing the module students should understand basic probability calculus. They should be familiar with a range of techniques for solving real life problems of the probabilistic nature.

1. Events, probabilities, random variables, distribution functions, probability density functions, discrete and continuous random variables, independence. Mean, variance and moments of random variables. Functions of a random variable. Some commonly used distributions: Binomial and Negative Binomial, Weibull, Normal, Log-Normal Normal, Gamma distributions. Special distributions in statistics: Chi-squared, t, F distributions.

2. Multivariate random variables: Joint, marginal and conditional distribution functions, Conditional expectations. Covariance of random variables. Bivariate Normal distribution and independence of bivariate Gaussian random variables.

3. Transformations of random variables: Use of direct methods and generating functions. Sum and ratio of two random variables.

4. Gen erating functions: moment and probability generating functions. Central limit theorem. Approximations. As illustrations of motivation by practical examples: Chi-squared etc.