Course co-ordinator(s): Dr Laila El Ghandour (Edinburgh), Dr Haslifah Hasim (Dubai).
Aims:
The aims of this course are
- To develop discrete probability models for data
- To understand important features of these models
Summary:
This course provides an introduction to some of the probability models for inference. The main topics covered are:
- Probability models: sample spaces and events; probability measures and their properties; simple probability calculations.
- Conditioning and Independence: conditional probability; `Chain Rule’ for computing probabilities; Bayes’ Theorem; Partition Theorem; independence of events; probability calculations using concepts of conditioning and independence.
- Random variables and their distributions, including the Binomial, Geometric, Poisson, Hypergeometric, and Indicator variables.
- Expectation and standard deviation of a random variable: definitions and properties of expectation and standard deviation.
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Location: Dubai, Edinburgh.
Semester: 2.
Syllabus:
1. Introduction to discrete probability models
- Models for random experiments:
- Sample spaces: events, set theory, Venn diagrams, de Morgan’s laws
- Probability functions and the axioms of probability: Choice of probability function, consequences of the axioms.
- Conditional probability and independence of events:
- Definitions of P(A|B) and the definition of independence
- `Chain rule’ for P(A intersection B)
- Bayes Theorem
- Partition Theorem and `tree diagrams’.
2. Special probability models for certain random experiments
- Simple equally likely models
- Sampling without replacement from a finite population:
- ordered samples: model assumptions, calculations and relevant counting arguments
- unordered samples: model assumptions, calculations and relevant counting arguments
- Building models for a sequence of independent sub
- experiments:
- General model assumptions
- Sampling with replacement: calculations and relevant counting arguments
- Bernoulli trials and Binomial models: calculations and relevant counting arguments
- Geometric models
- Other examples
3. Discrete random variables
- Definition of a discrete random variable
- Probability mass functions for discrete random variables
- Expectation and the properties of the expectation of a random variable.
- Variance and the properties of the variance of a random variable.
- Indicator variables
4. Special examples of discrete random variables.
- Binomial and Bernoulli variables
- Geometric and Negative Binomial variables
- Poisson variables
- Hypergeometric variables
- Indicator variables
Reading list:
A First Course in Probability by S.M.Ross, 7th ed. (Pearson 2006).
SCQF Level: 7.
Credits: 15.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the course leader.
Canvas: further information and course materials are available on Canvas