Distribution Calculators
Binomial and Poisson probabilities — point, cumulative, and tail — with expectation and variance, and the queried region highlighted on the distribution itself. Covers §6.15–6.17.
Binomial B(n, p)
X counts successes in n independent trials with success probability p each.
PMF of B(n, p); the queried region in red. FIG. T39-1
Poisson(λ)
X counts events in a fixed window when they arrive independently at mean rate λ.
PMF of Poisson(λ); the queried region in red. FIG. T39-2
Poisson is binomial's limit: with n huge, p tiny, and np = λ fixed, B(n, p) → Poisson(λ). That is why "rare events at a known average rate" always end up Poisson.