Question

If X and Y are any random variables with E(X) = 5, E(Y) = 6, E(XY) = 21, V(X) = 9 and V(Y) = 10, then the relationship between X and Y is a:
-strong positive relationship
-strong negative relationship
-weak positive relationship
-weak negative relationship

Answer 1

Answer:

We have a strong negative relationship between the variables.

Step-by-step explanation:

Given two random variables X and Y, it is possible to calculate the covariance as Cov(X, Y) = E(XY)-E(X)E(Y). We have E(X)=5, E(Y)=6 and E(XY)=21. Therefore Cov(X,Y)=21-(5)(6)=21-30=-9. On the other hand, we know that the correlation of X and Y is the number defined by $Cov(X,Y)/\sqrt{Var(X)}\sqrt{Var(Y)}$ and because in this particular case we have V(X)=9 and V(Y)=10, we have $-9/\sqrt{9}\sqrt{10}$ = -0.9487. Therefore, we have a strong negative relationship between the variables.