Comparing distributions
| Binomial | Geometric | Poisson | |
| written | X~B(n,p) | X~G(p) | X~Po{λ) |
| fixed number of independent trials | Number of trials until success | Number of arrivals in a fixed period | |
| E(x) | np | 1/p | λ |
| V(x) | np(1-p) | (1-p)/p2| λ | |
| Calculate in Excel | BINOMDIST(r,n,p,cum) | POISSON(r,λ,cum) |
The Excel functions have a parameter cumulative which is true if you want a cumulative distribution. This is P(X≤r), which is usually more useful than P(X=r).
There is no function for the geometric distribution. The probability is:
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