. 5. (a) Assume that X and Y are RVs given on a common probability space (12, F,P), E|X| 0, and set Z:= X + Y. For ne N, derive the conditional distributions P(X = k|Z = n), k = 0,1, 2, ..., and P(max{X, Y} = k|Z = 2n + 1), k = 0,1, 2, ... Hints: (d) Draw a picture! For what values of (X,Y) does one have Z = n? For what values of (X,Y) does one have max{X, Y} = k? For what values of (X,Y) does one have max{X, Y} = k and Z = 2n +1? . . 5. (a) Assume that X and Y are RVs given on a common probability space (12, F,P), E|X| 0, and set Z:= X + Y. For ne N, derive the conditional distributions P(X = k|Z = n), k = 0,1, 2, ..., and P(max{X, Y} = k|Z = 2n + 1), k = 0,1, 2, ... Hints: (d) Draw a picture! For what values of (X,Y) does one have Z = n? For what values of (X,Y) does one have max{X, Y} = k? For what values of (X,Y) does one have max{X, Y} = k and Z = 2n +1