Let the sample space S = {1, 2, 3}, P(i) = 1/3 for i = 1, 2, 3, and define random variablesX, Y , and Z as:X(1) = 1, X(2) = 2 X(3) = 3Y (1) = 2, Y (2) = 3 Y (3) = 1Z(1) = 3, Z(2) = 1 Z(3) = 2(a) Show that these three random variables have the same probability mass function.(b) Find the pmf of X + Y , Y + Z, and Z + X.(c) Find the pmf of X + Y Z, Z/|X Y |