An internet serviceprovider uses 50 modems to serve the needs of 1000 customers. It isestimated that at a given time, each customer will need aconnection with probability 0.01 independently of the othercustomers.

(a) What is the PMF of the number of modems in use at the giventime?
(b) Repeat part (a) by approximating the PMF of the number ofcustomers that need a connection with a Poisson PMF.
(c) What is the probability that there are more customers needing aconnection than there are modems? Provide an exact, as well as anapproximate formula based on the Poisson approximation of part(b).