A post office has three clerks, each of whom is serving a customer. The service times are i.i.d. Exp(µ). A new customer will arrive after Exp(λ) units of time, independently of the others. Find the probability that all the three existing customers finish their services before the arrival.
A post office has three clerks, each of whom is serving a customer. The service times are i.i.d. Exp(µ). A new customer will arrive after Exp(λ) units of time, independently of the others. Find the probability that all the three existing customers finish their services before the arrival.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 69E
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A post office has three clerks, each of whom is serving a customer. The service times are i.i.d. Exp(µ). A new customer will arrive after Exp(λ) units of time, independently of the others. Find the probability that all the three existing customers finish their services before the arrival.
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