Probability Distributions

Density, cumulative probability and quantiles for the five common distributions

Distribution

ParametersMean μStd dev σ

Normal

Overlay the CDF

Moments

Mean E(X)0

Variance Var(X)1

Std dev σ1

Query point x

Density f(x)0.241971

P(X ≤ x)0.841345

P(X > x)0.158655

Quantile

P(X ≤ k) = 0.951.6448535

Enter a probability between 0 and 1

Continuous densities are evaluated from the error and gamma functions, discrete ones by summing point masses; the quantile is the inverse CDF for continuous distributions and the smallest k with P(X ≤ k) ≥ p for discrete ones. Everything runs in your browser.