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LearnAQA7367First teaching 2017Paper 3 · Statistics optionPoisson distribution

Paper 3 · Module

Poisson distribution

3 subtopics≈ 100 min in total

Start the module: Poisson probabilities Open graphing calculator

Poisson probabilities
Rare, random events in a fixed interval, such as calls per hour, typos per page or meteors per night, follow the Poisson distribution. One number, the average rate $\lambda$ , sets everything: $P(X=r)=e^{-\lambda}\dfrac{\lambda^r}{r!}$ .
≈ 35 min
Scaling rates and sums
If events happen at $4$ per hour, they happen at $2$ per half-hour: scale $\lambda$ with the interval. And two independent Poisson streams combine into one, with the rates simply added.
≈ 30 min
Poisson and normal approximations
Two shortcuts. A binomial with many trials and a small success probability behaves like $\text{Po}(np)$ . A Poisson with a large mean behaves like $N(\lambda,\lambda)$ , as long as you remember the continuity correction.
≈ 35 min