Question: Telephone calls are being placed through an exchange at random times on an average of 12 calls per min. Assume the calls form a Poisson

Telephone calls are being placed through an exchange at random times on an average of 12 calls per min. Assume the calls form a Poisson process.

a) Determine the probability that there will be at most 3 calls in a 30-sec time period.

b) Derive the moment-generating function for the waiting time for the first call.

c) What is the probability that the wait time for the next phone call is more than one minute if the wait time has already been 30 seconds?

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