Probability

Geometric Distribution

Compute P(X=k) = (1−p)^(k−1)·p — the probability that the first success occurs on trial k. Includes CDF, mean 1/p, and variance.

Live Calculator · Step-by-Step · Probability

Inputs

p — probability of success (0 < p ≤ 1)

k — trial number (k ≥ 1)

Result

Enter values and calculate.

P(X = k)

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P(X ≤ k)

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= 1−(1−p)^k

P(X > k)

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= (1−p)^k

Mean μ

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= 1/p

Variance σ²

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= (1−p)/p²

Std Dev σ

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Step-by-Step Work

Your explanation will appear here.

Geometric PMF — P(X = k) for k = 1..20

Put It Into Practice

The calculator shows the steps — a quiz proves you can do them on your own.

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