AP®︎ Statistics (pre-2026): Topic 4.9 Flashcards

Master key terms and definitions for Topic 4.9 of AP Statistics (pre-2026) – Combining Random Variables 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This course has been archived.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

Linear Transformation of a Random Variable

Definition

Changing a variable by adding a constant, multiplying by a constant, or both.

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Linear Transformation of a Random Variable
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Changing a variable by adding a constant, multiplying by a constant, or both.

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Y = a + bX Transformation Rules
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Mean becomes a + bμx, standard deviation becomes |b|σx, and shape stays the same if b > 0.

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Linear Combination of Random Variables
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An expression formed by multiplying variables by constants and then adding them, like aX + bY.

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Mean of a Linear Combination
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For aX + bY, the mean is aμx + bμy.

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Independent Random Variables
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Two variables where knowing one value does not change the other's probability distribution.

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Mean of a Sum or Difference
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Add means for sums and subtract means for differences, keeping the order of subtraction.

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Effects of Linear Transformations
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Adding shifts center only, while multiplying changes center and spread and may reflect shape.

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Spread of Linear Combinations of Independent Variables
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For independent variables, variances add in sums or differences, then take the square root for standard deviation.

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