Blir throe categorical variables. X, Y and Z: (a) (5%) When Y is jointly independent of X and Z. ahow that X and 1are conditionally inde-pendent, given Z. (b) (5%) Prove that mutual independence of X, Y and Z implies that X and Iare both marginally and conditionally independent. (a) (5%) When X is independent of and Y is independent of Z. explain why XL is not necessarily independent of Z.
