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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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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7.3.2 The inter-recording time is a random sum with a geometric number of exponential terms and is exponential with parameter λp.
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.
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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