Statistical distributions (AS Unit 2: Applied Mathematics A) — WJEC A-Level Mathematics
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Statistical distributions (AS Unit 2: Applied Mathematics A) explained
Candidates must understand the operational conditions required to model real phenomena with three discrete distributions.
Read the full explanation
The binomial model X ~ B(n, p) applies when there is a fixed number of trials n, two mutually exclusive outcomes (success/failure), a constant probability of success p, and independent trials. The Poisson model X ~ Po(λ) models event counts in a fixed interval of space or time, assuming events occur singly, independently, and at a constant average rate λ. The discrete uniform distribution models n equally likely outcomes, each with probability 1/n, such as rolling an unbiased die.
Your focus
- State and verify the four assumptions required to model a scenario with a binomial distribution.
- Explain the conditions necessary for a Poisson process: constant average rate, independence, and events occurring singly.
- Identify scenarios where equally likely discrete outcomes justify a discrete uniform distribution.
Statistical distributions (AS Unit 2: Applied Mathematics A) exam tips
Marking Points
- stating the conditions for a binomial model: fixed n, independent trials, constant p, two outcomes
- stating the conditions for a Poisson model: constant rate, independent occurrences, events occurring singly
- identifying when a discrete uniform model applies due to equally likely outcomes
Examiner Tips
- 💡Memorise the exact conditions for binomial (fixed n, independent, constant p) and Poisson (singly, constant rate, independent).
- 💡State the distribution and its parameters explicitly, e.g. X ~ B(20, 0.4) or X ~ Po(3.5).
Common Mistakes
- applying a binomial model when sampling without replacement from a small population causes p to vary
- using a Poisson distribution when events cluster together rather than occurring singly and independently