statistics and probability

3. Let X1, X2, . .. he iid Exp) distributed. Think of these as times between arrivals of customers to a. postofoe. The rst customer arrives at T1 2 X1, the second at T2 2 X1 + X2, and so on. Let N he the number of arrivals in the interval [II], 1].| {a} Show that {N E n} = {Tn i 1}. (b) Show that the odf of T11 is given by "1 42 I: e [12:] FT"(17):1E T, mg. kz {C} Using (a) and (h), prove that N N Poi)