Solution Found!
Suppose that a company has determined that the the number
Chapter 5, Problem 139E(choose chapter or problem)
Suppose that a company has determined that the the number of jobs per week, \(N\), varies from week to week and has a Poisson distribution with mean \(\lambda\). The number of hours to complete each job, \(Y_{i}\), is gamma distributed with parameters \(\alpha \text { and } \beta\). The total time to complete all jobs in a week is \(T=\sum_{i=1}^{N} Y_{i}\). Note that \(T\) is the sum of a random number of random variables. What is
a \(E(T \mid N=n)\)
B \(E(T)\), the expected total time to complete all jobs?
Questions & Answers
(1 Reviews)
QUESTION:
Suppose that a company has determined that the the number of jobs per week, \(N\), varies from week to week and has a Poisson distribution with mean \(\lambda\). The number of hours to complete each job, \(Y_{i}\), is gamma distributed with parameters \(\alpha \text { and } \beta\). The total time to complete all jobs in a week is \(T=\sum_{i=1}^{N} Y_{i}\). Note that \(T\) is the sum of a random number of random variables. What is
a \(E(T \mid N=n)\)
B \(E(T)\), the expected total time to complete all jobs?
Step 1 of 3
Given that,
Suppose that a company has determined that the number of jobs per week, N, varies from week to week and has a Poisson distribution with mean \(\lambda\).
That is, \(E(N)=\lambda\)
The number of hours to complete each job, \(Y_{i}\) , is gamma distributed with parameters \(\alpha\) and \(\beta\). The total time to complete all jobs in a week is \(T=\sum_{i=1}^{N} Y_{i}\).
T is the sum of a random number of random variables.
Reviews
Review this written solution for 32005) viewed: 143 isbn: 9780495110811 | Mathematical Statistics With Applications - 7 Edition - Chapter 5 - Problem 139e
Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.
No thanks, I don't want to help other students