Consider a permitting office that is run by two clerks. Suppose that when Mr. Edge enters the system, he discovers that Mr. Made is being served by one of the clerks and Mr. Green by the other. Mr. Edge is told that his service will begin as soon as either Green or Made leaves. Also, it is known that the amount of time that a clerk spends with a customer is exponentially distributed with mean 1/lambda.

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Consider a permitting office that is run by two clerks. Suppose that when Mr. Edge enters the system, he discovers that Mr. Made is being served by one of the clerks and Mr. Green by the other. Mr. Edge is told that his service will begin as soon as either Green or Made leaves. Also, it is known that the amount of time that a clerk spends with a customer is exponentially distributed with mean 1/lambda.


Question 3a: Define the random variables in this situation; for each random variable, explain all possible outcomes (the sample space).
Question 3b: What is the probability that, of the three customers, Mr. Edge is the last to leave the post office? Please show the mathematical expressions and explain your solution

 

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