Each millisecond at a telephone switch, a call independently arrives with probability p. Each call is either a data call(d) with probability q or a voice call (v). Each data call is a fax call with probability r. Let N equal the number of milliseconds required to observe the first 100 fax calls. Let T equal the number of milliseconds you observe the switch waiting for the first fax call. Find the marginal PMF PT (t) and the conditional PMF P_N|T (n|t). Lastly, find the conditional PMF P_T|N (t|n).