4.12 The Geometric Distribution

Part of Probability, Random Variables, and Probability Distributions in AP® Statistics. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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The Geometric Setting

The geometric distribution

Conditions (BIPS):

Binary: each trial has two outcomes (success/failure)
Independent: trials are independent
Probability same: probability of success ${p}$ is constant
Stopping rule: we count the number of trials until the FIRST success

${X \sim \text{Geom}(p)}$ where ${X}$ = number of trials until first success

Key difference from binomial: In the binomial, the number of trials ${n}$ is fixed. In the geometric, we keep going until we get a success — the number of trials is the random variable.

Example: Roll a die until you get a 6. ${X}$ = number of rolls needed. ${p = 1/6}$ .

In this unit

12 lessons

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