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Combining Independent Random Variables — Mean and Variance Rules

μ_{X+Y} = μ_X + μ_Y. For independent X,Y: σ²_{X+Y} = σ²_X + σ²_Y (variances always add, NOT standard deviations).

StatisticsCommon Core VAR-5.CPROBVerified correct ✓

Worked examples

Random variables X and Y are independent with E(X) = 7 and E(Y) = 11. Find E(2X + 1Y).
Answer: 25
Random variables X and Y are independent with E(X) = 20 and E(Y) = 6. Find E(2X + 2Y).
Answer: 52

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