Geometric Distribution Calculator

From a success probability p and a number of failures k, compute the geometric distribution probability mass P(X=k), cumulative probability, upper tail, mean, and variance, with a bar chart.

Input

From the success probability p and the number of failures k, compute the geometric distribution probability mass, cumulative distribution, upper tail, mean, and variance.

Number of failures k (non-negative integer)

Enter the number of failures k before the first success.

Success probability p (greater than 0 and at most 1)

Enter the probability of success p on a single trial.

Result

Probability mass P(X = k) (k = 2, success probability 0.3)

0.147

Cumulative P(X at most k) (lower tail)

0.657

Upper tail P(X greater than k)

0.343

Mean

2.33333333

Variance

7.77777778

Probability mass function PMF bar chart

How it works

The geometric distribution models the number of failures k before the first success, when each trial is independent with a constant success probability. This tool uses the k = 0, 1, 2, ... definition.
The probability mass is computed as P(X = k) = (1 − p)^k × p.
The cumulative distribution (lower tail) is P(X ≤ k) = 1 − (1 − p)^(k + 1), and the upper tail is P(X greater than k) = (1 − p)^(k + 1).
The mean is (1 − p) / p and the variance is (1 − p) / p².
Enter a success probability p greater than 0 and at most 1, and a number of failures k that is a non-negative integer.

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