[Basic Probability]Consider a joint distribution onX, Y, with Prob(X=i, Y=j) =pij, whereX {1,2}andY {1,2,3}. This is summarized in the following table:Y= 1Y= 2Y= 3X= 1p11p12p13X= 2p21p22p23Assumepijare all positive. In the following, write your answers in terms of elementsof the joint distribution above.(a) Calculate the marginal distribution Prob(X= 2) and Prob(Y= 1).(b) Calculate Prob(Y= 1|X= 2).(c) Calculate the probability Prob(X < Y), whereX < Yis the event that the valueofXis smaller than the value ofY