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Geometric Distribution PMF Calculator

Probability that the first success occurs on trial k.

Compute P(X = k), the probability that the first success in a Bernoulli sequence occurs on trial k, using the shifted geometric distribution P = (1 − p)^(k − 1) · p. Reports the mean 1/p and variance (1−p)/p².

Daniel Oh By Daniel Oh
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 − p)^(k − 1) · p; mean = 1/p; var = (1 − p)/p².

In depth

Compute P(X = k), the probability that the first success in a Bernoulli sequence occurs on trial k, using the shifted geometric distribution P = (1 − p)^(k − 1) · p. Reports the mean 1/p and variance (1−p)/p².