Statistics

Beta Distribution Calculator

Find the mean, variance and mode of a beta distribution.

Calculated Output

Mean 0.2857

Variance 0.0255

Mode 0.2

Formula: mean = α/(α+β)

Step-by-Step Breakdown

1. Values used:

2. Alpha (α) = 2

3. Beta (β) = 5

5. Mean = 0.2857

6. Variance = 0.0255

7. Mode = 0.2

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The math behind it

mean = α/(α+β), variance = αβ/((α+β)²(α+β+1)), mode = (α−1)/(α+β−2) for α,β > 1.

α 2, β 5 → mean 0.286, mode 0.20.

Why is it useful?

It's the conjugate prior for the binomial — central to Bayesian inference.