AP®︎ Statistics: Topic 2.9 Flashcards

Master key terms and definitions for Topic 2.9 of AP Statistics – Parameters of Random Variables to help you prep for quizzes and the AP exam.

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Term

Parameter

Definition

Numerical characteristic of a probability distribution or population; a single fixed value

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Parameter
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Numerical characteristic of a probability distribution or population; a single fixed value

2.9.A2.9.A.1
Expected Value / Mean of a Discrete Random Variable
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E(X) or μ_X; the probability-weighted average of possible values, μ_X = Σ x_i P(X = x_i)

2.9.A2.9.A.2
Interpretation of Expected Value
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Over many repetitions of the random process, the long-run average value of the random variable is approximately μ_X, in context and units

2.9.B2.9.A.2
Variance of a Discrete Random Variable
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V(X), Var(X), or σ_X²; V(X) = Σ (x_i - μ_X)² P(X = x_i)

2.9.A2.9.A.3
Standard Deviation of a Discrete Random Variable
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SD(X) or σ_X; σ_X = √(Σ (x_i - μ_X)² P(X = x_i)), the typical distance of values from the mean

2.9.A2.9.A.3
Interpretation of Standard Deviation
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Over many repetitions, values of the random variable typically differ from the mean by about σ_X, in context and units

2.9.B2.9.B.1
Equivalent Variance Formula
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V(X) = E(X²) - [E(X)]², where E(X²) = Σ x_i² P(X = x_i)

2.9.A2.9.A.3
Units of Mean, Variance, and Standard Deviation
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Mean and standard deviation have the same units as X; variance has squared units

2.9.B2.9.B.1