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Geometric Distribution Calculator

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Geometric Distribution: Definition, Formula, and Examples

Geometric Distribution

Definition: The geometric distribution models the number of trials needed to achieve the first success in a sequence of independent Bernoulli trials, where each trial has the same probability of success.

Formula:P(X=k)=p(1p)k1P(X = k) = p(1-p)^{k-1}

Where:

  • kk is the number of trials until first success
  • pp is the probability of success on each trial

Properties

  • Mean: E(X)=1pE(X) = \frac{1} {p}
  • Variance: Var(X)=1pp2Var(X) = \frac{1 - p} {p ^ 2}
  • Support: k=1,2,3,...k = 1, 2, 3, ...

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