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Module PROBABILITY & STATISTICS

Module code: EE304
Credits: 5
Semester: 1
Department: THEORETICAL PHYSICS
International: Yes
Coordinator: Joost Slingerland (THEORETICAL PHYSICS)
Overview Overview
 

Indicative Syllabus
Probability Theory
Introduction to Probability Theory and Forms of Data Presentation - Contingency Tables
Review of Basic Set Theory
Definition of Events in terms of sets
Complementary and Mutually Exclusive Events.
Interpretation of Probability in terms of relative frequencies.
Axioms of Probability Theory
Addition Formula for probability
Conditional Probability
Bayes Theorem and Law of Total Probability
Concept of Independent Events
Network Problems and Determination of Reliability of Networks
Counting Techniques and Application to Sample Spaces with large numbers of sample points
Discrete Random Variables and the Probability mass function
Special Discrete Probability Distributions Binomial, Poisson Distribution
Application of Poisson distribution to engineering problems - Queuing Theory
Expected Value and Variance, Chebychev's Inequality
Continuous Random Variables (Probability Density Function and Cumulative Distribution Function)
Properties of a probability density, expected value and variance.
The Gaussian (Normal) distribution and its properties and importance in application.
The exponential distribution and its relation to the Poisson process and queuing theory
The Gamma distribution and the Weibull Distribution and their application to modelling times to failure
Statistics
Introduction to Statistics Inference and Estimation of Parameters.
The central limit theorem.
Large/Small Sample confidence interval estimates for the population mean and the T-distribution.
Large Sample confidence interval estimates for a population proportion.
Introduction to hypothesis testing and the idea behind the process.
Hypothesis testing on a population mean (large and small samples).
Hypothesis testing on a population proportion (large sample).
Categorical Data: Chi-squared goodness of fit test. Chi-squared independence test.
Simple Linear Regression. Correlation/Causation. Prediction Intervals. Hypothesis testing.
Discussion of relation of studied material to simple engineering experiment design.

Open Learning Outcomes
 
Open Teaching & Learning methods
 
Open Assessment
 
Open Repeat options
 
Open Pre-Requisites
 
Open Co-Requisites
 
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