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 independently of the other customers.(adsbygoogle = window.adsbygoogle || []).push({});

(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) What 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).

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# What is the PMF of the number of modems in use at the given time?

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