Let fx,yz(x, y, z) = 3* rle(1+z)y > y > 0, xe {0, 1, 2, 3, 4, 5, ....), ze {1, 2, 3, 4, 5, ....} and =0 otherwise, be the mixed (Discrete & Continuous) joint PDF of (X, Y, Z) (a) Compute Marginal PDF of Y , Joint PDF(PMF) of X and Z, and Margianl PMF of Z (Hint:).-0 2 1 So f(x, y, z ) dy = 1) (b) Compute Conditional pmf(pdf) of Y given Z = z and Var(Y Z=E(Z) ) E(Z) (c) Compute Conditional pmf(pdf) of X given (Y = y, Z = 2) and Compute Var(2X |Y = 5, Z = 2) (d) Compute E(ex|Y = 5, Z =1) and E(II-o(X - k)|Y = 4, Z = 2) (Ex: [Ik-o(X - k) = X(X - 1)(X -2))