5.1.4 Customers arrive at a service facility according to a Poisson process of rate customer/hour. Let X(t) be the number of customers that have arrived up to time t. (a) What is Pr{X(t)=k} for k = 0, 1,...? (b) Consider fixed times 0
5.1.4 Customers arrive at a service facility according to a Poisson process of rate customer/hour. Let X(t) be the number of customers that have arrived up to time t. (a) What is Pr{X(t)=k} for k = 0, 1,...? (b) Consider fixed times 0
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![5.1.4 Customers arrive at a service facility according to a Poisson process of rate
customer/hour. Let X(t) be the number of customers that have arrived up to
time t.
(a) What is Pr{X(t)=k} for k = 0, 1,...?
(b) Consider fixed times 0<s<t. Determine the conditional probability
Pr{X(t)=n+k|X(s) = n} and the expected value E[X(t)X(s)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2F5af64a32-2373-4acc-87bc-a60ab382a62b%2F1r6n1lw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.1.4 Customers arrive at a service facility according to a Poisson process of rate
customer/hour. Let X(t) be the number of customers that have arrived up to
time t.
(a) What is Pr{X(t)=k} for k = 0, 1,...?
(b) Consider fixed times 0<s<t. Determine the conditional probability
Pr{X(t)=n+k|X(s) = n} and the expected value E[X(t)X(s)].
![5.1.4 (a)
(at)ke-λt
k!
k = 0, 1, ...;
(b) Pr{X(t)=n+k\X(s) = n} = [(t−s)]ke¯(-s)
E[X(t)X(s)]=²ts +λs.
k!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2F5af64a32-2373-4acc-87bc-a60ab382a62b%2Fjassxi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.1.4 (a)
(at)ke-λt
k!
k = 0, 1, ...;
(b) Pr{X(t)=n+k\X(s) = n} = [(t−s)]ke¯(-s)
E[X(t)X(s)]=²ts +λs.
k!
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