Suppose that customers arrive at a telco service centre according to a Poisson process having rate = 2 per minute. Let () be the number of customers that arrived up to time , whereby t is measured in minutes.

(a) Determine the following probabilities and conditional probabilities.

i. Pr{(1) = 2}

ii. Pr{(1) = 2 and (3) = 6}

iii. Pr{(3) = 6|(1) = 2}

(b) Determine [(2)].

(c) If the service centre can handle at most 5 customers per minute, what is the probability that the facility will receive more customers than it can handle during a specified one-minute interval?