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Question

For a certain person, the daily number of telephone calls (incoming or outgoing) has a Poisson distribution with mean 12. The length in time (in minutes) of each telephone call has an exponential distribution with mean 5 minutes. The length of time of one telephone call is independent of the length of time of any other telephone call.

1. What is the probability that this person makes 5 telephone calls and received another 8 telephone calls in 1 ½  days?
2. On a given day, this person makes or receives 4 telephone calls. What is the probability that this person is on the telephone for more than half an hour? 

 

Answer 1

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