Consider the random variable T defined in the previous problem (i.e., the first arrival). Suppose that, as you're looking at your watch, you note that you've already been waiting for t hours and the first arrival has still not occurred. How does this influence the amount of time that you still have to wait? Problem 3.1. Prove that for any t > 0, PT > t+ sT > t] = P[T > s]. In words: The probability that you have to wait at least s more hours for the first arrival after observing that T' > t is the same as the probability that you had to wait at least s hours to begin with