Consider a process where independent, memoryless "events" (or "arrivals") happen randomly in time. Let Si be the arrival time of the ith event (so So = 0) and let E1, E2,... be iid Exp(\) variables where Ek is the time between the (k 1)st and kth arrival. Then - Sn ~ E+ + En ~ Gamma(n, \) Let be the number of arrivals that occur up through time t. Show that Nt ~ Pois(\t). Hint: If there are k arrivals in (0,t], when must the k + 1st arrival occur?