If X and Y are random variables with Var(X)= 7.5,Var(Y)= 6 and Cov(X,Y)= 4,then Var(2X + 3Y)is:
A)33
B)37
C)88
D)132

Question

Quizplus · Accepted Answer

The variance of a linear combination of two random variables $X$ and $Y$, $Var(aX + bY)$, is given by $a^2Var(X) + b^2Var(Y) + 2abCov(X,Y)$. Substituting the given values, we get $Var(2X + 3Y) = 2^2 \times 7.5 + 3^2 \times 6 + 2 \times 2 \times 3 \times 4 = 30 + 54 + 48 = 132$.

If X and Y Are Random Variables with Var(X)= 7