In a multi-user operating system, requests for a particular resource arrive at an average rate of 20 per hour (a Poisson arrival process). What is the probability that no request is made in a 45-minute interval?

Explanation

For a Poisson arrival process with rate λ = 20 requests/hour, the expected number of arrivals in a window of length t (in hours) is λt. A 45-minute window is t = 0.75 hour, so the expected number of arrivals is 20 × 0.75 = 15. The probability of exactly zero arrivals in a Poisson process with mean m is e^(−m), so here it is e^(−15), option (i); options (iii) and (iv) wrongly give the probability of at least one arrival instead of none.