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LearnEdexcel9FM0First teaching 2017Option · Further Statistics 1Poisson and binomial distributions

Option · Module

Poisson and binomial distributions

4 subtopics≈ 140 min in total

Start the module: The binomial distribution Open graphing calculator

The binomial distribution
Count the successes in $n$ independent trials, each with the same chance $p$ . The probability of exactly $r$ successes is $\binom nr p^r(1-p)^{n-r}$ : choose which trials succeed, then multiply.
≈ 40 min
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