Let X and Y are two discrete random variable with pmf P(X) and P(Y), respectively, where both variables take value: 0,1,2,..500. Clearly define the value of each following random variable and Provide a simplified expression for the expected value and standard derivation:

a) (Pt: 5): Z1= X+Y

b) (Pt: 5): Z2= X-Y

c) (Pt-5): Z3=XY

d) (Pt: 5): Z4= X/Y.

e) (Pt: 5): Z5= |X-Y|