Problem 9(Exponential Distribution) Suppose that every three months, on average, an earthquake occurs in California

(a) What is the probability that an earthquake will not occur for another year?

(b) What is the probability that the next earthquake occurs after 3 but before 7 months?

Problem 10(Exponential Distribution) Guests arrive at a hotel, in accordnce with a Poisson Process, at a rate of 5 per hour Suppose that for the last 10 minutes no guest has arrived What is the probability that

(a) The next one will arrive in less than 2 minutes?

(b) From the arrival of the 10th to the arrival of the 11th guest takes no more than 2 minutes?