Problem 6 Consider two independent experiments whose random outcomes X and Y are in the sample space (0, 1, 2,...}. The probability assignments for X and Y are given by 1 27 PIX = 1] = and e . i! PLY = j] = 2 . j! (i) (6 pts.) Show that both assignments are valid pmfs. (ii) (8 pts.) Determine PIX + Y = k], for k > 0. The binomial theorem is useful here. (iii) (6 pts.) Given that X + Y = k, what are the possible values of X? What is the conditional probability of each of those values