The arrivals of new telephone calls at a telephone switching office is a Poisson process N(t) with an arrival rate of λ = 4 calls per second. An experiment consists of monitoring the switching office and recording N(t) over a 10-second interval.
(a) What is PN(1)(0), the probability of no phone calls in the first second of observation?
(b) What is PN(1)(4), the probability of exactly four calls arriving in the first second of observation?
(c) What is PN(2)(2), the probability of exactly two calls arriving in the first two seconds?