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## PROBABILITY AND STATISTICS

Module code: EE304FZ
Credits: 5
Semester: 1
Department: INTERNATIONAL ENGINEERING COLLEGE
International:
Overview

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
• 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.

Learning Outcomes

Teaching & Learning methods

Assessment

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