1. Permutations and Combinations (1.1 Examples of Permutations with small sets, 1.2 Permutations with Restrictions and repetitions, 1.3 Understand what combinations are and how they differ from permutations, 1.4 Combinations with restrictions)
2. Set theory for discrete sample spaces (2.1 Definition of a set, 2.2 Elements and membership, 2.3 Set notation, 2.4 Types of sets: finite, infinite, equal, and equivalent sets, 2.5 Subsets and Power Sets, 2.6 Union, intersection, difference relative complement, and complement, 2.7 Venn diagrams to visualise set operations, 2.8 De Morgan's Laws, 2.9 Countable and uncountable sets)
3. Probability theory (3.1 Definition of probability, 3.2 Sample space and events, 3.3 Probability of an event, 3.4 Complement rule, 3.5 Addition rule for mutually exclusive events, 3.6 General addition rule, 3.7 Definition of conditional probability, 3.8 Bayes Theorem, 3.9 Concept of independence, 3.10 Multiplication rule for independent events, 3.11 Counting and probability Frequentist approach, 3.12 Introduction to subjectivist and Bayesian approaches to probability)
4. Cumulative distribution functions and density functions of discrete random variables (4.1 Definition of cdf and density function of discrete random variables, 4.2 Models for a sequence of independent sub-experiments, including Bernoulli trials, Binomial and Geometric models, 4.3 Details of Hypergeometric, and Poisson models)
5. Expected Value and Variance (5.1 Definitions and Simple problems, 5.2 Indicator functions, 5.3 Linear combinations of two rvs)
6. Advanced topics (6.1 CLT, 6.2 LLN, 6.3 binomial to Normal)
By the end of the course, students should be able to do the following:
Curriculum explorer: Click here
SCQF Level: 7
Credits: 15