If X and Y are two variables with σ_x = 3.8,σ_y = 4.2,and COV(X,Y)= −0.25,then V(X + Y)= 31.58.

Question

Quizplus · Accepted Answer

We can use the formula for the variance of the sum of two random variables: V(X + Y) = V(X) + V(Y) + 2COV(X,Y) Plugging in the given values: V(X + Y) = σ_x + σ_y + 2COV(X,Y) V(X + Y) = 3.8 + 4.2 + 2(-0.25) V(X + Y) = 7.6 - 0.5 V(X + Y) = 7.1 Therefore, V(X + Y) = 31.58 is false, and the correct value is V(X + Y) = 7.1. So the answer is A.

If X and Y Are Two Variables with σx =

If X and Y Are Two Variables with σ_x =