1. The joint probability distribution of two discrete random variables X and Y are given by the following joint probability mass function:
P( X=x, Y=y ) = k | x – y |, x = 1, 2, 3 ; y = 2, 4, 5
= 0, otherwise.
(a) Find the constant k
(b) Find the marginal distributions of X and Y
(c) Calculate the correlation coefficient between X and Y
(d) Are X and Y Independent ?