stats

Binomial Distribution

P(X=k), CDF, tail areas, and PMF bar chart for n trials at probability p — normal approximation overlay.

Parameters

Trials n

Success probability p

Evaluation Mode

Successes k

Results

P(X = k)—

P(X ≤ k) — CDF—

P(X ≥ k)—

P(X > k)—

P(X < k)—

Mean = np—

Variance = np(1−p)—

Std Dev—

P(X=k) = C(n,k)·p^k·(1−p)^(n−k) · log-space via lgamma

ln C(n,k) via lgamma — avoids overflow for large n
Normal overlay when np ≥ 5 and n(1−p) ≥ 5