Customers arrive at a service facility according to a Poisson process of rate A = 7 customers/hour. Let N(t) be the number of customers that have arrived up to time t hours. Let W₁, W2, W3, ... be the successive arrival times of the customers. (a) Find the expected arrival time of the 10-th customer, E[W₁0] = hours (b) Given N (3) = 3, determine the expected arrival time of the 10-th customer, E[W₁0 | N(3) = 3] = hours.

A First Course in Probability (10th Edition)
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Customers arrive at a service facility according to a Poisson process of rate λ = 7 customers/hour. Let N(t) be the
number of customers that have arrived up to time t hours. Let W₁, W2, W3, ... be the successive arrival times of the
customers.
(a) Find the expected arrival time of the 10-th customer, E[W₁0] :
=
hours
(b) Given N(3) = 3, determine the expected arrival time of the 10-th customer, E[W₁0 | N(3) = 3] =
hours.
Transcribed Image Text:Customers arrive at a service facility according to a Poisson process of rate λ = 7 customers/hour. Let N(t) be the number of customers that have arrived up to time t hours. Let W₁, W2, W3, ... be the successive arrival times of the customers. (a) Find the expected arrival time of the 10-th customer, E[W₁0] : = hours (b) Given N(3) = 3, determine the expected arrival time of the 10-th customer, E[W₁0 | N(3) = 3] = hours.
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