Suppose that patients arrive at the emergency room of a hosp

Suppose that patients arrive at the emergency room of a hospital according to a Poisson process at the rate of = 5 per hour. The probability that exactly 10 patients come in the next 2 hours is 0.12511. Given that exactly 10 patients come in the 2 hours, the probability that exactly 20 patients come in the next 4 hours is 0.12511.

a.) Let T be the time between the 10th and 20th patients. Find the distribution of T