If X and Y are independent variables with V(X)= 23.48 and V(Y)= 36.52,then the standard deviation of W = X + Y is σ_w = 7.746.

Question

Quizplus · Accepted Answer

If X and Y are independent, then the variance of the sum will equal the sum of the variances:

V(X+Y) = V(X) + V(Y) = 23.48 + 36.52 = 60

Therefore, the standard deviation of W = X + Y is:

sigma_W = sqrt(V(X+Y)) = sqrt(60) = 7.746

Since this matches the given value, the answer is true.

If X and Y Are Independent Variables with V(X)= 23