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 ?