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Rasheed Wallace is a very good, but emotionally unbalanced, basketball player. We model this as follows (allowing scores to be non-integral): For each minute that he plays, his team outscores its opponent by 0.25 points. For each minute that he does not play, his team is outscored by 0.5 points. He is charged with personal fouls in a time-homogenous manner at a rate of one foul per eight minutes. On other words, his personal fouls form a continuous-time arrival process that is a Poisson process with parameter = 1/8 (with all times measured in minutes). Any time he commits a sixth personal foul in a game, he loses his temper, gets three technical fouls, and is ejected from the game; this costs his team 6 points in addition to the fact that he does not play the remainder of the game. Except where indicated below, assume Wallace plays from the beginning of the game until the end of the game or ejection. Basketball games are 48 minutes long and since we have a continuous (non-integral) model for scores we need not consider the possibility of a tie at the end of 48 minutes. (a) Let Xt denote the number of personal fouls Wallace has committed t minutes from the beginning of the game. Determine the PMF of Xt. (b) What is the probability that Wallace fouls out of a game? (c) What is the probability that Wallace's team wins? (d) To help Wallace rehabilitate his image, his new coach Larry Brown decides to remove Wallaceimmediately and for the rest of the gamewhenever he commits a fifth foul in a game. (Wallace thus nevers fouls out, nor loses his temper, nor gets technical fouls.) Now what is the probability that Wallace's team wins?