An article in Ad Hoc Networks discussed an underwater acoustic sensor network to monitor a given area in an ocean. The network does not use cables and does not interfere with shipping activities. The arrival of clusters of signals generated by the same pulse is taken as a Poisson arrival process with a mean of ? per unit time. Suppose that for a specific underwater acoustic sensor network, this Poisson process has a rate of 2.5 arrivals per unit time.

a) What is the mean time between 2.0 consecutive arrivals?

b) What is the probability that there are no arrivals within 0.3 time units?

c) What is the probability that the time until the first arrival exceeds 1.0 units of time?

d) Determine the mean arrival rate such that the probability is 0.9 that there are no arrivals in 0.3 time units.