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Discrete Uniform Distribution Probability Calculator

P(X=k) = 1/n for integers a to b.

Calculates probability mass, mean μ = (a+b)/2, variance σ² = (n²−1)/12, and P(X ≤ k) for a discrete uniform distribution over integers from a to b.

Nadia Almasri By Nadia Almasri
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

P(X=k) = 1/(b−a+1); μ = (a+b)/2; σ² = ((b−a+1)²−1)/12

In depth

Calculates probability mass, mean μ = (a+b)/2, variance σ² = (n²−1)/12, and P(X ≤ k) for a discrete uniform distribution over integers from a to b.