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22 -1zy2 5. (20 points) Let fx,y,z(x, y, z) = 3% xle(1+z)y , y > 0, x E {0, 1, 2, 3, 4, 5, ....}, z E {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: Ex-0 Ez-1 0 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 = z) and Compute Var(2X |Y = 5, Z = 2) (d) Compute E(exly = 5, Z = 1) and E(II,-o(X - k)|Y = 4, Z =2) (Ex: [Ik=o( X - k) = X(X - 1) (X -2))