7.3.2 The inter-recording time is a random sum with a geometric number of exponential terms and is exponential with parameter λp. Equation 7.7 E[WN(t)+1]={M(t) + 1}. (7.7) 7.3.2 A fundamental identity involving the renewal function, valid for all renewal processes, is E[WN(0)+1]=E[X] (M(t) + 1). See equation (7.7). Evaluate the left side and verify the identity when the renewal counting process is a Poisson process.
7.3.2 The inter-recording time is a random sum with a geometric number of exponential terms and is exponential with parameter λp. Equation 7.7 E[WN(t)+1]={M(t) + 1}. (7.7) 7.3.2 A fundamental identity involving the renewal function, valid for all renewal processes, is E[WN(0)+1]=E[X] (M(t) + 1). See equation (7.7). Evaluate the left side and verify the identity when the renewal counting process is a Poisson process.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 44E
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Please do the following questions with handwritten working out. The answer is in the image.
Transcribed Image Text:7.3.2 The inter-recording time is a random sum with a geometric number of exponential terms
and is exponential with parameter λp.
![Equation 7.7
E[WN(t)+1]={M(t) + 1}.
(7.7)
7.3.2 A fundamental identity involving the renewal function, valid for all renewal
processes, is
E[WN(0)+1]=E[X] (M(t) + 1).
See equation (7.7). Evaluate the left side and verify the identity when the
renewal counting process is a Poisson process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2F995c4eb8-2afd-427f-94fc-8fae40ec6777%2Fi7kpwpo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Equation 7.7
E[WN(t)+1]={M(t) + 1}.
(7.7)
7.3.2 A fundamental identity involving the renewal function, valid for all renewal
processes, is
E[WN(0)+1]=E[X] (M(t) + 1).
See equation (7.7). Evaluate the left side and verify the identity when the
renewal counting process is a Poisson process.
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