S_D = {0, 1, 2, 4, 5, 7, 8} where

d₁ = 0, d₂ = 1, d₃ = 2, d₄ = 4, d₅ = 5, d₆ = 7, d₇ = 8.

Consider the bivariate PMF: =y, (x, y) {(di, d;), i,je {1, 2, 3,4} } fo(z,y) = cdz x ty, (x, y) E {(di, d;), i, je {1, 2,3, 4}} (Note, constructing a table might be useful here) A) Calculate the appropriate value of c. B) Find the two marginal PMFs fx (@), fy (y) and determine whether X and Y are independent. C) Calculate E[X] and Var(X) D) Find fxy=d (x | y = d3) E) Calculate E[X | Y = d3] and Var(X | Y = d3). F) Use E[X | Y = dx] to construct E[ X], verifying your calculation in part (C). G) Find P[Y > X]