Second Year Stastics Modules – Department Of Mathematical Sciences

Second Year Statistics Modules

Title	Distribution Theory
Code	SSTT111, SSTT112	Department	Mathematical Sciences
Prerequisites	None	Co-requisites	SMTH111, SMTH112, SMTH221
Aim	To introduce fundamental continuous distributions and their properties which will be used in Statistical Inference and which will form the foundation for all third year level statistics modules.
Content	Random variables of the continuous type; Continuous distributions – probability density function, cumulative distribution function, and moments; Special continuous distributions; Distributions of functions of random variables; Mixed distributions; Distributions of two continuous random variables; Correlation coefficients; Marginal distributions; Conditional distributions; The bivariate normal distribution; Transformations of random variables; Independent random variables; Distributions of sums of independent random variables; Random functions associated with the normal distribution; Approximations for discrete distributions; The central limit theorem; Limiting distributions; Chebychev’s inequality and convergence in probability.
Assessment	40% Continuous Assessment Mark 60% Formal end of module exam (3 hours)
DP Requirement	40% Continuous Assessment Mark 80% Attendance at lectures and tutorials.

Title	Statistical Inference
Code	SSTT212	Department	Mathematical Sciences
Prerequisites	SSTT111, SSTT112	Co-requisites	SSTT211, SMTH221, SMTH222
Aim	To introduce students to estimation, and parametric- and nonparametric hypothesis tests.
Content	Order statistics; Maximum likelihood, methods-of-moments, and ordinary least squares estimation methods; Properties of estimation; Point estimation of means, variances, proportions, and differences; Sampling distributions; Confidence intervals for means, variances, proportions, and differences; Sample size calculations; Distribution-free confidence intervals; Simple linear regression point- and interval estimation of regression parameters; Hypothesis tests for single parameters (mean, variance, proportion, and regression parameters) and differences (between means, variances, proportions, and regression parameters); Contingency tables – goodness-of-fit test, and test for independence; Introduction to ANOVA; Nonparametric tests – Wilcoxon, Kolmogorov-Smirnov, and Runs test; Sufficient statistics; Power of a statistical test; Best critical regions; Uniformly most powerful tests; Likelihood ratio tests.
Assessment	40% Continuous Assessment Mark 60% Formal end of module exam (3 hours)
DP Requirement	40% Continuous Assessment Mark 80% Attendance at lectures and tutorials.