Let fxyz,T(x,y,z,t) = e -(2x+4y+z+2t)/2 otherwise, be the joint PDF of (X, Y, Z,T) (a) Compute 1 P{X 0,t > 0, and -0 (b) Compute E[(2X+Y+4T+2Z) | (E(Z+ Y)=x+27)] (c) Are X.T.Y.Z are mutually independent? Explain why they are indepedent or why they are not independent. (d) Find the pdf of K and variance of K, where K = X+T+cdY, c=Var(Z) &d=E(Y) (e) Compute E[4X2X | >] and Var[Y-E(Z) | 0 Y=T+Z > 2}