If the random variables T and U have the same joint probability function at the following five pairs of outcomes: (0, 0), (0, 2), (-1, 0), (1, 1), and (-1, 2). What is the covariance of T and U?
σxy = E(XY) - μx⋅μy
The Attempt at a Solution
My issue with this problem is interpreting what is meant by each of the points having the same joint probability function. The only way I am able to proceed is by considering that the joint probability function (whatever that may be for the two variables) evaluated at each of the five outcomes returns the same value. In other words, each of the five outcomes listed above have an equal probability of occurring. I am able to find the covariance if this is the case.
Is this interpretation of the problem statement correct? If not, what is the proper interpretation? I have no difficulty with the mathematical operations associated with this problem, I'm just not sure if I'm understanding the problem statement.
Any help is appreciated.