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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
Related questions
Question
Please do the following questions with full handwritten working out. The answer is in the image
![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!
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,