Requests for a product arrive to a storage facility according to a Poisson process with rate λ per hour. Given that n requests are made in a t-hour time interval, find the probability that at least k...

Requests for a product arrive to a storage facility according to a Poisson process with rate λ per hour. Given that n requests are made in a t-hour time interval, find the probability that at least k requests were made in the first hour. Is this conditional probability different if the beginning of the one-hour period is chosen according to a probability density f(s) on the interval [0, t − 1]?