2. Let X and Y be discrete random variables with the following pmfs: 0 1 2 -1 0 P(X = x) .3 2 .5 P( Y = y) .3 4 .3 Let the random variable Z be defined as X + Y. (a) What is the support of Z? (b) Find the pmf of Z, and verify that _; P(Z = zi) = 1 for all z; in the support of Z. (c) What is E(Z)? Check that this is equal to E(X) + E(Y)