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Variables X and Y take values x1,...,xn and y1,...,yn with yi = a*xi + b for each i. Which relation between their variances holds?

1. Var(Y) = a² Var(X)
2. Var(Y) = a² Var(X) + b
3. Var(Y) = Var(X) + b
4. None of these

Correct answer: Var(Y) = a² Var(X)

Solution

Variance is unaffected by an additive constant and is multiplied by the square of the scale factor, so Var(Y) = a² Var(X).

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