How to use this calculator
Pick the distribution, enter its parameters, and choose what to find: P(X = x), P(X ≤ x), P(X ≥ x), a range, or the value at a given cumulative probability.
Formulas
PoissonP(X = x) = e−λλx/x!, μ = σ² = λ
ExponentialP(X ≤ x) = 1 − e−λx, μ = 1/λ
WeibullF(x) = 1 − exp[−(x/δ)β]
HypergeometricP(X = x) = C(K, x)C(N − K, n − x)/C(N, n)
Worked example
Flaws on a wire average 2.3 per mm: P(exactly 2 in 1 mm) (the default; Montgomery Example 3-31)
- X is Poisson with λ = 2.3.
- P(X = 2) = e−2.3(2.3)²/2! = 0.265.
- The mean and the variance are both 2.3.
Frequently asked questions
When is the Poisson distribution right?
For counts of independent events in a fixed interval of time, length or area, at a constant average rate.
Why is P(X = x) zero for the exponential?
For a continuous variable any single value has zero probability; only intervals have positive probability.