Problem 1

Suppose that car accident in a given town have a Poisson distribution, with an average of 5 per week (i.e. = 5). Also, note that, given a Poisson process with mean , the waiting time until the first outcome has an exponential distribution with mean 1/.

a) What is the probability that more than 6 accidents occur in a given week?

b) What is the probability that the time until an accident will be at least one week?

c) Suppose that no accidents have occurred for two weeks. What is the probability that no accidents will occur for another two weeks? Give the exact value or round your answer to six decimal places.