Consider a bank office where two clerks, A and B, are working. Service times of Clerks A and B are exponential with rate

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answerhappygod
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Consider a bank office where two clerks, A and B, are working. Service times of Clerks A and B are exponential with rate

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Consider a bank office where two clerks, A and B, are working.
Service times of Clerks A and B are exponential with rates
πœ‡π΄ per hour and πœ‡π΅ per hour, respectively. When you
arrive at the office, there are three customers, two (Customers 1
and 2) being served and one (Customer 3) waiting. You just joined
the waiting line.
a. Express the expected waiting time of Customer 3 using
πœ‡π΄ and πœ‡π΅.
b. Express your expected total time in the office (including
your service time)?
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