Module overview
The main aim of the module is to provide the students with necessary knowledge of statistics and stochastic processes to carry out simple statistical procedures and to be able to develop simulation and other models widely employed in OR. The model is split into two parts: Statistics and Stochastic Processes.
One of the pre-requisites for MATH6158
Aims and Objectives
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
- State and apply the Central Limit Theorem.
- Conduct simple regression analysis and basic ANOVA tests and assess the applicability of the models used to the data. Interpret and present the results of the statistical techniques taught on the module
- Define a number of common distributions, fit them to data and test the goodness of fit.
- Derive confidence intervals for mean and variance and compare the means and variances using appropriate hypothesis tests.
- Display technical material on a poster. Have a working knowledge of MINITAB.
Syllabus
Statistics
1. Introduction; Organizing and displaying data; Summary measures.
2. Probability distributions; Discrete random variables: Binomial distribution; Poisson distribution;
Geometric and Negative Binomial distributions.
3. Continuous random variables: Exponential distribution; Gamma distribution; Normal distributions; QQ-plot.
4. Sampling distribution; Estimation and confidence intervals: Central Limit Theorem; parameter estimation (method of moments); confidence interval for mean; comparison of two means; introduction to hypothesis testing; Chi-Square Tests.
5. Regression and analysis of variance: simple regression and basic ANOVA tests.
6. Practical statistics: the use of Minitab to analyse data and the interpretation of the results.
7. Design of technical posters.
Stochastic Processes
1. Discrete time Markov chains: determining the state space; classification of states; finite absorbing chains; finite ergodic chains; general finite chains.
2. Continuous time Markov chains: global and detailed balance; forward and backward equations; birth-death chains. Poisson processes. Semi-Markov chains.
Learning and Teaching
Teaching and learning methods
Twenty-two 2-hour lectures
Eleven 1-hour problem class sessions
| Type | Hours |
|---|---|
| Independent Study | 86 |
| Teaching | 64 |
| Total study time | 150 |
Resources & Reading list
Textbooks
DLP Minh (2001). Applied Probability Models (core text). Duxbury.
DR Stirzaker (2005). Stochastic Processes and Models. Oxford University Press.
PG Hoel (1947). Introduction to Mathematical Statistics. Wiley.
RE Walpole & RH Mayers (1972). Probability and Statistics for Engineers and Scientists. Macmillan.
PS Mann (2006). Introductory Statistics. John Wiley & Sons.
Assessment
Assessment strategy
The summative coursework will be on Statistics (one individual assignment that includes production of a poster).
Referral/repeat assessment is by both examination and coursework, but if a pass is obtained in the original coursework, the coursework mark will be carried forward without possibility of referral/repeat.
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Coursework | 30% |
| Closed book Examination | 70% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Coursework | 30% |
| Examination | 70% |
Repeat Information
Repeat type: Internal & External