(5 points each.) Captain Phasma is pursuing an escaping BB-8. The number of shots she fires from her blaster, N, is uniformly distributed on [0, 1, 2, 3, 4]. Each shot she fires has probability 2 of hitting BB-8. BB-8 starts with 3 health, and each hit takes one point off his life (he cannot have negative health). Let H be the health of BB-8 after Phasma has fired all her shots. a) Compute the joint PMF PNH (x, y). Represent your answer as a table. b) Compute the joint CDF FNH(x, y). Represent your answer as a 2D piecewise constant function (i.e., divide the XY-plane into grid squares and indicate the height of the CDF at each point). c) Compute the marginal PMF PH(y). Represent your answer as a table. d) Compute the probability that BB-8's health is the same as the number of shots Phasma fired