Suppose you arrive at a bus stop at time 0, and at the end of each minute,with probability p one bus arrives, or with probability 1 p no busarrives. Whenever a bus arrives, you board that bus with probability qand depart. Let T denotes the number of minutes you wait at the busstop, and N be the number of buses that arrive while you wait at the busstop.(a) Find range of (N, T), that is the set of all points (n, t) for whichPN,T (n, t) > 0.(b) Find PN,T (n, t).(c) Find the marginal PMFs PN (n) and PT (t).(d) Find the conditional PMFs PN|T (n|t) and PT|N (t|n).(e) Are T and N independent?