Please provide details on steps used to solve the problem below. A maintenance unit receives requests from three branches of a company: A, B and C. Suppose that the requests from each branch come according to separate independent Poisson processes. The average time between requests from branches A, B and C is 5 minutes, 10 minutes and 30 seconds respectively. It has been 5 minutes since the last request from branch A, 12 minutes from branch B and 3 minutes from branch C. i. What is the expected time until the next request? ii. What is the probability that the next request will be from branch B?

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Please provide details on steps used to solve the problem below.

A maintenance unit receives requests from three branches of a company: A, B and C. Suppose that the requests from each branch come according to separate independent Poisson processes. The average time between requests from branches A, B and C is 5 minutes, 10 minutes and 30 seconds respectively. It has been 5 minutes since the last request from branch A, 12 minutes from branch B and 3 minutes from branch C.

i. What is the expected time until the next request?
ii. What is the probability that the next request will be from branch B?

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