Advanced Math (a) Suppose X, Y, Z:2R are three discrete random variables. Prove that (Px py) Pz Px (py pz). This says that the convolution product is associative. (b) Suppose X and Y are discrete...

Extracted text: Advanced Math (a) Suppose X, Y, Z:2R are three discrete random variables. Prove that (Px py) Pz Px (py pz). This says that the convolution product is associative. (b) Suppose X and Y are discrete random variables with X Bin(4, ) and Y ~ Bin(5, ). Using the definition of convolution, calculate px + py. (Vandermonde's identity may be useful here.) Can Kou Gnd y quick way of deing this calculation by thinking of Y and Y ax indenendent random