Local calls are coming into a telephone exchange according, Basic Statistics

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Local calls are coming into a telephone exchange according

Question: Local calls are coming into a telephone exchange according to a Poisson process with rate λdis calls per minute. Independently of this, long-distance calls are coming in at a rate of λ_dis calls per minute. Write down expressions for probabilities of the following events:

a) Exactly 5 local calls and 3 long distance calls come in a given minute:

b) Exactly 50 calls (counting both local and long distance) come in a given three minute period:

c) Starting from a fixed time, the first ten calls to arrive are local.

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