First Year Modules

Stream: BSc - Marthematical Statistics

Credits: 15

Module Content

Probability concepts. 
Sample point method. 
Event composition method. 
Conditional probability. 
Bayes’ Theorem. 
Random variable theory. 
Special discrete distributions: Binomial, Geometric, Negative Binomial, Hypergeometric & Poisson and Normal. 
Moments & MGF’s. 
Factorial moments and PGF’s.

Stream: BSc - Mathematical Statistics

Credit: 15

Pre-requisites

STAS101 (at least 40%)

Module Content

Basic probability concepts. 
Theory of continuous probability distributions. 
Expected values and MGF. 
Special continuous probability distributions: Uniform, Gamma, Exponential, Weibull, Pareto and Normal. 
Theory of multivariate discrete and continuous distributions, marginal and conditional distributions. 
Co-variance and correlation. 
Theory of conditional expectation and conditional variance. 
Functions of random variables: distribution function technique, transformation methods, MGF technique. Limiting distributions and stochastic convergence. 
CLT and applications.  Sampling distributions: Chi-square, t, F, Beta distributions. 
Monte Carlo simulation.

Stream: BCom - Statistics

Credits: 12

Module Content

Simple and compound interest, nominal and effective interest rate
Continuous compounding, changes in interest rate
Net present value and internal rate of return.
Simple and complex annuities, growing annuities
Perpetuities and growing perpetuities.
Loans: outstanding balance, interest and principal portion of instalment, missed payments, changes interest rates.
Depreciation and sinking funds.
Linear programming: graphical/corner point method.
Sensitivity analysis.

Stream: BCom - Statistics

Credit: 12

Module Content

Stream: BA

Credits: 7

Module Content

Introduction to statistics: population, sample, sampling, scientific method, design of research studies, scales of measurement, discrete and continuous variables, statistical notation
Frequency distributions: tables, graphs (bar chart, histogram, frequency polygon, pie chart and scatterplot), shape of frequency distributions
Central tendency: mode, median and mode
Variability: range, semi-inter-quartile range, variance, standard deviation
z-Scores: calculating z-scores and deriving standardised distributions based on z-scores
Probability: ratio between the number of specific outcomes and the total number of possible outcomes, range between 0 and 1, probability of the unit normal distribution
The distribution of sample means: samples and sampling error, probability of obtaining a range of sample means, standard error of the mean, the central limit theorem and the law of large numbers
Introduction to hypothesis testing: the logic, uncertainty and error in hypothesis testing, the general elements of hypothesis testing, one- and two-tailed tests, the z test
One- and two-sample (independent) t tests
Estimation: point estimates and confidence intervals for the mean
Correlation and simple linear regression
Chi-square tests for goodness of fit and independence