Random Variables and Probability Distributions
Purpose: The background material introduced the concepts of experiments, but analysing them further requires a bit of work. Random variables turn the experiment into something mathematical, while probability distributions explain how often the outcomes happen. We use several past exam questions to demonstrate these concepts.
Topics Covered: We explain the concept of a random variable and the two different types; discrete and continuous. We then introduce the functions used to measure the distribution of probabilities. We discuss ways of measuring averages and variability. We delve into specific examples of distributions, some you may have seen before (Binomial, Normal) and others you may have not (Uniform, Poisson, Exponential).
Intended Learning Outcomes: You may not understand what a random variable exactly is (it's quite nebulous), but you should understand the difference between discrete and continuous random variables, along with the functions determining their probability. You should learn what a cumulative distribution function is and what it does. You should learn how to calculate simple expectations and variances. You should see several examples of distributions and where to use them.
Random Variables and Probability Distributions Refresher
Useful Links:
2024 AQA Maths Paper 3: Need for Questions 15 and 17
2023 AQA Further Maths Statistics Paper: Need for Questions 6 and 8
2019 AQA Further Maths Statistics Paper: Need for Questions 1 and 8
2020 AQA Further Maths Statistics Paper (Nov): Need for Questions 1 and 4
STEP Past Papers: The 2023 exams can be found in a zip folder. Need for Q11.
Sections
Tree Diagrams and Conditional Probability
Contact
stats dot ug dot support at warwick dot ac dot uk