Course Content (Syllabus)
A. PROBABILITY
Theory of sets and probability,(events, axioms of probability, conditional probability, Bayes' theorem, combinatorial analysis, tree diagrams) - random variables - probability distributions (discrete and continuous probability distributions, joint distributions, independent random variables, change of variables, convolutions) - mathematical expectation - variance and standard deviation - functions of random variables - standardised random variables - covariance - correlation coefficient - Chebyshev's inequality and the law of large numbers - specific probability distributions (binomial, normal, Poisson, uniform, Cauchy, gamma, chi-square and Student's distributions, relations between distributions, central limit theorem).
B. STATISTICS
Sampling theory (population and sample, random samples, sampling distributions, population parameters (means, proportions, differences, sums), sample statistics (sample mean, sample variance) - estimation theory (confidence intervals for means, proportions, differences, sums, variances) - tests of hypotheses and significance (statistical hypotheses, type I and type II errors, level of significance, one- and two-sided tests, special tests of significance, fitting of theoretical to sample frequency distributions, chi-square test, contigency tables) - curve fitting (regression, least squares method, standard error of estimate, multiple regression, linear and generalised correlation coefficient, sampling theory of regression and correlation).