An internet service provider uses 50 modems to serve the

QUESTION:

An internet service provider uses 50 modems to serve the needs of 1000 customers. It is estimated that at a given time. each customer will need a connection with probability 0.01, independent of the other customers. (a) What is the PMF of the number of modems in use at the given time? (b) Repeat part (a) by approximating the PMF of the number of customers that need a connection with a Poisson PMF. (c) \Vhat is the probability that there are more customers needing a connection than there are modems? Provide an exact. as well as an approximate formula based on the Poisson approximation of part (b) .