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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. One of the pre-requisites for MATH6158

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 problem class sessions

TypeHours
Teaching64
Independent Study86
Total study time150

Resources & Reading list

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

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

PG Hoel (1947). Introduction to Mathematical Statistics. 

DR Stirzaker (2005). Stochastic Processes and Models. 

PS Mann (2006). Introductory Statistics. 

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

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

Referral

MethodPercentage contribution
Coursework 30%
Examination 70%

Repeat Information

Repeat type: Internal & External

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