8. Starting at time 0, customers arrive at a service counter in accordance with a Poisson process of rate A (customers per hour). Assume that each customer requires exactly 1 hour of service, and that the number of servers is unlimited. Fix t > 1. (a) Find the probability that there are no customers being served at time t. (b) Find the expected number of customers being served at time t.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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8. Starting at time 0, customers arrive at a service counter in accordance with a Poisson process
of rate A (customers per hour). Assume that each customer requires exactly 1 hour of service, and
that the number of servers is unlimited. Fix t > 1.
(a) Find the probability that there are no customers being served at time t.
(b) Find the expected number of customers being served at time t.
Transcribed Image Text:8. Starting at time 0, customers arrive at a service counter in accordance with a Poisson process of rate A (customers per hour). Assume that each customer requires exactly 1 hour of service, and that the number of servers is unlimited. Fix t > 1. (a) Find the probability that there are no customers being served at time t. (b) Find the expected number of customers being served at time t.
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