An insurance company feels that each of its policyholders has a rating value and that a policyholder having rating value λ will make claims at times distributed according to a Poisson process with rate λ, when time is mea- sured in years. The ?rm also believes that rating values vary from policyholder to policyholder, with the probability distribution of the value of a new policyholder being uniformly distributed over (0, 1). Given that a policyholder has made n claims in his or her ?rst t years, what is the conditional distribution of the time until the policyholder's next claim?