Discrete probability distributions.
Build and interpret discrete probability models, from individual random variables to binomial counts, with worked methods, contextual decisions and six progressively demanding papers.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Random variables and probability tables
Turn uncertain outcomes into numerical variables and build valid probability tables.
- 02
Probability functions and cumulative probabilities
Move between a probability function and cumulative probabilities, paying attention to strict inequalities.
- 03
Expected value
Calculate long-run averages and use them to assess fair prices and expected returns.
- 04
Variance and standard deviation
Measure spread using a probability distribution and distinguish variance from standard deviation.
- 05
Effects of scale/shift
Track how converting units, changing a fee or reversing a scale changes a distribution’s mean and spread.
- 06
Sums of independent variables
Combine independent random quantities without confusing the mean of a sum with its spread.
- 07
Bernoulli trials
Use a 0–1 success indicator to model one trial and connect it to repeated-trial counts.
- 08
Binomial assumptions
Decide when a fixed count of trials can genuinely be modelled by a binomial distribution.
- 09
Binomial probabilities and cumulative probabilities
Translate exact, cumulative and complementary wording into reliable binomial calculations.
- 10
Binomial mean/variance
Use binomial summaries and reverse them to find model parameters when possible.
- 11
Interpreting distribution results
Use probability results to make measured decisions and explain what a distribution does—and does not—predict.
Topic review
Revisit the key ideas, then choose a practice paper.