9. A manufacturer has many machines that all do the same task. These machines break down at random times. Let N(t) be the number of machines that break in the time interval (0, t]. Assume that N (t ) is a Poisson process at rate 1.5 per week. Determine: (a) the probability that 3 machines break in a two-week interval. (b) the expected number of breakdowns in a four-week interval. (c) the probability of 3 breakdowns in the first two weeks and 6 breakdowns in the first 5 weeks. (d) the probability that the first breakdown occurs within the first week. (e) the probability that the third breakdown occurs within the first 8 weeks