This module introduces probability theory, random variables, probability distributions and statistical inference. The fundamental laws of probability including Bayes' theorem are covered. Motivating random variables as a mapping of experimental results onto subsets of the real numbers, this module covers the mathematics of probability including the standard univariate discrete and continuous distributions. Statistical inference for population means/proportions are also covered.
Probability Theory
Axioms of probability. Addition rule. Independence. Conditional probability. Multiplication rule. Bayes’ Theorem. Counting rules, including permutation and combinations.
Discrete Random Variables
Probability distributions and mass functions. Expected values and variances. Functions of random variables. The Bernoulli, binomial, multinomial, geometric, negative binomial and Poisson distributions; their expectations/variances.
Continuous Random Variables
Probability density functions. Expected values and variances. Functions of a continuous random variable. The uniform, exponential and normal distributions; their means and variances.
Statistical Inference
The Central Limit Theorem. Hypothesis tests for population means/proportions. Confidence intervals for population means/proportions.
Lectures supported by tutorials and computer laboratory sessions.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |