The University of Southampton
Courses

MATH6006 Statistical Methods

Module Overview

The main aim of the module is to provide the students, who may have no previous knowledge of statistics or stochastic processes, with sufficient knowledge of these subjects to carry out simple statistical procedures, and to develop simple stochastic models. The module is split into two parts: statistics and stochastic processes.

Aims and Objectives

Module Aims

The main aim of the module is to provide the students, who may have no previous knowledge of statistics or stochastic processes, with sufficient knowledge of these subjects to carry out simple statistical procedures, and to develop simple stochastic models. The module is split into two parts: statistics and stochastic processes.

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

  • Define a number of common distributions, fit them to data and test the goodness of fit.
  • State and apply the Central Limit Theorem.
  • Derive confidence intervals for mean and variance and compare the means and variances using appropriate hypothesis tests.
  • 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
  • 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 PC sessions

TypeHours
Independent Study95
Teaching55
Total study time150

Resources & Reading list

DR Stirzaker (2005). Stochastic Processes and Models. 

DLP Minh (2001). Applied Probability Models (core text). 

PS Mann (2006). Introductory Statistics. 

RE Walpole & RH Mayers (1972). Probability and Statistics for Engineers and Scientists. 

PG Hoel (1947). Introduction to Mathematical Statistics. 

Assessment

Assessment Strategy

The repeat assessment includes both coursework and examination. If the coursework was previously passed, it is not retaken.

Summative

MethodPercentage contribution
Closed book Examination  (2 hours) 70%
Coursework 30%

Referral

MethodPercentage contribution
Coursework 30%
Exam 70%

Costs

Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.

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