5. Practice problem-will not be graded: (Continuing Problem 5 from HW #4) In the Internet, messages (e.g.. emails) are broken into smaller pieces, called packets, before being transmitted. Packets are lost at a router (switch) due to limited buffer (physical memory) at the router. Let T, i 1, 2, . . .. denote the time at which i-th packet loss occurs with To = 0 and = T-T,-1 be the inter-loss time between the i-th and (i-1).th packet losses. Suppose that the inter-loss times X"-1,2-.. , are independent and exponentially distributed with parameter , ie., Xi ~ exponential(A) for all (a) Let N(T) denote the number of packet losses over [0. T].T>0. Show that N(T)~Poisson(A {T, 1 and Tz > 1). Given B. what is the conditional distribution of T. (b) Suppose that B i.e., FTB (c) Suppose that each packet loss belongs to either customer 1 with probability p, 0