Poisson Probability Mass Function & CDF

A Poisson variable counts how many times a rare event happens in a fixed window, given it happens at an average rate lambda. Unlike Binomial, there's no fixed number of trials — events can happen any number of times.

P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!}

Task: write poisson_pmf_cdf(lam, k) returning [pmf, cdf], each rounded to 4 decimal places, where cdf = P(X \le k).

lam is the rate λ — the expected number of events in the window.
When k is close to lam, the pmf sits near its peak — that's the most likely single outcome.

Poisson Probability Mass Function & CDF

Examples

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