F78PA - Probability and Statistics A

Course leader(s):

• Paul Dobson (Edinburgh, September)
• Eric Nimako Aidoo (Dubai, September)
• Sarat Chandra Dass (Malaysia, September)
• Lawrence John O'Brien (Malaysia, September)

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 mass and density functions, calculating probabilities using these functions, transformations, and properties of these functions.

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. Joint probability, density, and distribution functions; marginal and conditional distributions; expectation of a function of random variables; covariance; correlation; conditional expectation and its uses.

7. Markov’s inequality, Chebyshev’s inequality, and introduction to the Central Limit Theorem with applications to statistics.

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 probability mass functions, probability density functions, and cumulative distribution functions.
• apply transformation methods to determine the distribution function, probability function, probability, expected value, and variance for a random variable.
• compute the conditional and marginal distributions, as well as their properties, from bivariate random variables.
• evaluate the relationship between bivariate random variables using their covariance and correlation.
• apply Markov’s and Chebyshev’s inequalities, as well as the Central Limit Theorem, to approximate probabilities of a random variable.

Further details

Curriculum explorer: Click here

SCQF Level: 8

Credits: 15