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 measured in years. The firm 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 first t years, what is the conditional distribution of the time until the policyholder’s next claim?