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

The X and Y variables have a strong negative relationship.

Step-by-step explanation:

The X and Y variables have a strong negative relationship. This can be determined by analyzing the correlation coefficient, which indicates the strength and direction of the relationship between two variables.

In this case, since the correlation coefficient is significantly different from zero (positive or negative), we can conclude that there is a significant linear relationship between X and Y. The fact that the correlation coefficient is negative indicates that as X increases, Y tends to decrease, and vice versa.

Therefore, the correct answer is strong negative relationship.

Answer 2

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)/√(Var(X))√(Var(Y))` and because in this particular case we have V(X)=9 and V(Y)=10, we have
`-9/√(9)√(10)` = -0.9487. Therefore, we have a strong negative relationship between the variables.