Question

1. Assume that q and z are two random variables that are perfectly positively correlated. q takes the value of 20 with probability 0.5 and the value of zero with probability 0.5, while z takes the value of 10 with probability 0.5 and the value of zero with probability 0.5. What is the covariance of q and z?

(A) 50.
(B) 100.
(C) 0.
(D) 1.
(E) There is not enough information to tell.

Answer 1

You state that q and z are perfectly positively correlated. This alone says the covariance of q and z is 1. The rest of the information you provide is a red herring.

Answer 2

Thank you for responding. The solution, however, is shown as 100. Wouldn't the coorelation coefficient be 1 but not necessarily the covariance?