Variance Algebra
Mathematical rules for variance: Var(aX+b) = a²Var(X), Var(X+Y) = Var(X)+Var(Y) when independent, and Var(X-Y) = Var(X)+Var(Y) when independent.
Real World
A fund manager at Vanguard uses Var(X + Y) = Var(X) + Var(Y) to estimate the combined risk of two uncorrelated stock holdings — a key principle behind portfolio diversification.
Exam Focus
Remember adding or subtracting a constant never changes variance; confusing Var(X − Y) with Var(X) − Var(Y) is the most common error.
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