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 a population mean/proportion are also covered. Descriptive statistics and data visualisation are briefly reviewed.
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. Statistical tests for a population mean/proportion. Confidence intervals for a population mean/proportion.
Lectures supported by tutorials and computer lab sessions.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |