Geometric distribution

Definition

A geometric distribution describes the number of trials needed for a single success in a sequence of independent Bernoulli trials. Each trial has the same probability of success.

5 Must Know Facts For Your Next Test

1. The probability mass function (PMF) of a geometric distribution is $P(X = k) = (1 - p)^{k-1} p$ where $k$ is the trial number and $p$ is the probability of success.
2. The expected value (mean) of a geometric distribution is $E(X) = \frac{1}{p}$.
3. The variance of a geometric distribution is $Var(X) = \frac{1 - p}{p^2}$.
4. A geometric distribution assumes that each trial is independent and has only two possible outcomes: success or failure.
5. The cumulative distribution function (CDF) for a geometric distribution is $F(k; p) = 1 - (1 - p)^k$.

Review Questions

• What is the formula for the probability mass function (PMF) of a geometric distribution?
• How do you calculate the expected value for a geometric distribution?
• What assumptions must hold true for data to follow a geometric distribution?

Related terms

Bernoulli Trial:

An experiment or process that results in a binary outcome: success or failure.

Binomial Distribution:

A discrete probability distribution describing the number of successes in a fixed number of independent Bernoulli trials.

Poisson Distribution:

A discrete probability distribution expressing the probability of a given number of events occurring in a fixed interval of time or space.