AP®︎ Statistics (pre-2026): Topic 4.12 Flashcards

Master key terms and definitions for Topic 4.12 of AP Statistics (pre-2026) – The Geometric Distribution to help you prep for quizzes and the AP exam.

This course has been archived. The College Board updated AP Statistics for the 2026–27 school year, and the units and topics changed.
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Term

Geometric Random Variable

Definition

A discrete variable counting the trial number on which the first success occurs.

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Geometric Random Variable
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A discrete variable counting the trial number on which the first success occurs.

UNC-3.EUNC-3.E.1
Conditions For A Geometric Distribution
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Independent trials, two outcomes, constant success probability p, and interest in the first success.

UNC-3.EUNC-3.E.1
Geometric Probability Function
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P(X = x) = (1 - p)^(x - 1)p for x = 1, 2, 3, ....

UNC-3.EUNC-3.E.2
Mean Of A Geometric Distribution
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The expected number of trials until the first success, equal to 1/p.

UNC-3.FUNC-3.F.1
Standard Deviation Of A Geometric Distribution
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The spread in trials until the first success, equal to sqrt(1 - p)/p.

UNC-3.FUNC-3.F.1
Possible Values Of A Geometric Random Variable
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Positive integers 1, 2, 3, ... because the first success can occur on any trial.

UNC-3.EUNC-3.E.1
Binomial Vs. Geometric Distribution
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Binomial counts successes in n fixed trials; geometric counts trials until the first success.

UNC-3.E
Contextual Interpretation Of Geometric Parameters
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Describe mean or standard deviation as numbers of trials until the first success in context.

UNC-3.GUNC-3.G.1
Shape Of A Geometric Distribution
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Always skewed right, with larger trial numbers becoming progressively less likely.

UNC-3.G