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.
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.
Thank you for responding. The solution, however, is shown as 100. Wouldn't the coorelation coefficient be 1 but not necessarily the covariance?
To find the covariance of two random variables, you need to know their individual means and probabilities, as well as their correlation. In this case, we are given the probabilities and values of the random variables, but not their means.
The covariance (Cov) of two random variables q and z is given by the formula:
Cov(q, z) = E[(q - E[q]) * (z - E[z])]
Since we do not have the means E[q] and E[z], we cannot calculate the covariance directly. Therefore, we cannot determine the value of the covariance of q and z in this specific case.
Hence, the correct answer is (E) There is not enough information to tell.