What are the assumptions which a process needs to satisfy to qualify as having

a Poisson distribution?

(b) Arrivals at a post office may be modelled as following a Poisson distribution

with a rate parameter of 78 arrivals per hour. Find:

i. the probability of exactly six arrivals in a period of two minutes

ii. the probability of more than two arrivals in 90 seconds

iii. the probability that the time to arrival of the next customer is less than

one minute.

(c) If D is the time to arrival of the next customer, calculate:

P(D > 1.9 | D > 1).