F78ZA - Fundamentals of Probability

Course leader(s):

Aims

To introduce basic ideas related to probability models
To introduce a number of specific probability distributions and illustrate their applications

Syllabus

1. Probability models – sample spaces, events, random variables, probability measures, axioms and properties

2. Conditional probability and independence including chain rule, partition rule, Bayes’ Theorem and applications, uses of independence

3. Random variables and their distributions – distribution, probability and density functions, transformations

4. Expectation, variance, and standard deviation of random variables, alternative calculations

5. Important special distributions and their main properties: Bernoulli, Binomial, Geometric, Poisson, Uniform, Normal, Exponential, Gamma.

6. Random Variables: General Theory - Computing probabilities, expected value and variance using a distribution function, properties of distribution functions, application of independent random variables

Learning outcomes

By the end of the course, students should be able to do the following:

Compute the probability, mean, and variance for discrete and continuous random variables using their respective probability mass functions and probability density functions.
Apply transformation methods to determine the distribution function, probability function, probability, expected value, and variance for a random variable.

Further details

Curriculum explorer: Click here

SCQF Level: 8

Credits: 7.5