Conference participants arrive at the registration desk at a rate = 30 arrivals/hour. The time between consecutive arrivals is exponentially-distributed. The number of arrivals in a given period is a Poisson RV. Let X denote the inter-arrival time (between consecutive arrivals).

a) Find the probability Prob(3 min X 6 min).

b) Given that we had 1 arrival in the past 2 minutes, find the probability of 1 arrival in the

next 3 minutes.

c) Find the probability of having 3 arrivals in the interval between 10-to-20 minutes.