1)Dr. Turner is reviewing her patient notes from the visits she had today. However, she is on-call and will receive pages that require immediate attention. Pages come at a Pois- son rate of 4 pages per hour. What is the probability that in 30 minutes, Dr. Turner will receive at least 1 page?

2)Let {N (t), t 0} be a Poisson process with rate . Let Sn denote the time of the nth event.

(a) (5 points) Find E[S15].

(b) (5 points) Find E[S7|N (3) = 2].

(c) (5 points) Find E[N (40) N (30)|N (10) = 15].