3. (12 marks) The average number of lightning strikes on transformers during the severe thunderstorm season in a given area is four per three weeks (i.e., 4/3 per week). Assume that a Poisson process is in operation. Find the probability that during the next storm season: (a) one must wait at most 1 week in order to see the first transformer strike (3 marks) (b) one must wait at least 2 weeks and at most 3 weeks in order to see the first transformer strike (c) there are more than 4 transformer strikes in three weeks (d) there is exactly 8 transformer strike in six weeks (3 marks) (3 marks) (3 marks)