3. The two teams of the FC-ICE and the InterHOT play a mini soccer match. The goals from each team are modeled as a Poisson process, independent of each other. The FCICE is assumed to score 2 goals/30 minutes on average while the InterHOT l goal/30 minutes. This game has regulation times of the rst and second half, 30 minutes each. This is the second match of their home-andaway tournament. The rst match was scoreless. Therefore, if they are still scoreless during the regulation, they play the extra time of 30 minutes. If still scoreless after the extra time, they play a shootout. {Atlkelt You may use P(k, t) : for the probability that a Poisson process has k arrivals for the duration of t or P(T1 0) for the probability that the interarrival time for the Poisson process is less than t. Of course, you should specify your 3L clearly. (a) What is the probability that both teams play extra time? (b) What is the probability that both teams play extra time but no shoot out? (c) What is the expected number of goals from the FCICE? You do not count a shootout goal after extra time. (d) What is the expected total time of this match? Again, you do not count shoot-out time