Track 5 · Probability Distributions · Lesson 4 of 10
The Poisson distribution
Calculate Poisson probabilities for counts in an interval, scale the rate to the interval length, and check whether count data really behave like a Poisson model.
A contact centre must decide how many agents to roster for each hour; an insurer must price policies by how many claims to expect. Both start from the same question — how many events will happen in a fixed stretch of time or space? — and the Poisson distribution is the first model to try. Knowing when it fails matters just as much.
The Poisson distribution models the number of events in a fixed interval — calls in an hour, typing errors on a page, claims in a policy year — when events happen one at a time, independently, at a steady average rate. Unlike the binomial, there is no fixed number of trials: in principle can be without an upper limit.
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It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Calculate Poisson probabilities for exactly, at most and at least k events
- Rescale the rate λ to the length of the interval and use SD = √λ
- Estimate λ from data and check the model with the dispersion index
- Explain why overdispersion arises and why it makes a Poisson model overconfident