If Z is a random variable generated by adding together X and Y which are also random variables,what do we know about var(Z)if X and Y are positively correlated.? A)var(Z)= var(X)+ var(Y) B)var(Z) var(X)+ var(Y) D)var(Z)= var(X)* var(Y)

Question

If Z is a random variable generated by adding together X and Y which are also random variables,what do we know about var(Z)if X and Y are positively correlated.?
A)var(Z)= var(X)+ var(Y)
B)var(Z)< var(X)+ var(Y)
C)var(Z)> var(X)+ var(Y)
D)var(Z)= var(X)* var(Y)

Quizplus · Accepted Answer

When X and Y are positively correlated, they tend to move together in the same direction. Therefore, when added together to form Z, they amplify each other's effect on the variance. This leads to the variance of Z being greater than the sum of the variances of X and Y, i.e., var(Z) > var(X) + var(Y).

If Z Is a Random Variable Generated by Adding Together