Let the random variables X and Y have the joint pmf
(a) p(x, y) = 1/3, (x, y) = (0, 0), (1, 1), (2, 2), zero elsewhere.
(b) p(x, y) = 1/3, (x, y) = (0, 2), (1, 1), (2, 0), zero elsewhere.
(c) p(x, y) = 1/3, (x, y) = (0, 0), (1, 1), (2, 0), zero elsewhere.
In each case compute the correlation coefficient of X and Y.