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Let {N(1), t z 0} be a nonhomogeneous Poisson process with intensity function A(1), t20 However, suppose one starts observing the process at a random time 7 having distrıbution function F. Let N*(t) = N(T + t) - N(7) denote the number of events that occur in the first t time units of observation %3D (a) Does the process {N*(t), t = 0} possess independent increments? (b) Repeat (a) when {N(t), t 2 0} is a Poisson process.

Let {N(1), t z 0} be a nonhomogeneous Poisson process with intensity function A(1), t20 However, suppose one starts observing the process at a random time 7 having distrıbution function F. Let N*(t) = N(T + t) - N(7) denote the number of events that occur in the first t time units of observation %3D (a) Does the process {N*(t), t = 0} possess independent increments? (b) Repeat (a) when {N(t), t 2 0} 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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Let {N(1), t 2 0} be a nonhomogene ous Poisson process with intensity function A(t), t20 However, suppose one starts observing the process at a random time r having distribution function F. Let N*(1) = N(T + t) - N(7) denote the number of events that occur in the first t time units of observation (a) Does the process {N*(?), t> 0} possess independent increments? (b) Repeat (a) when {N(t), t 2 0} is a Poisson process.
Transcribed Image Text:Let {N(1), t 2 0} be a nonhomogene ous Poisson process with intensity function A(t), t20 However, suppose one starts observing the process at a random time r having distribution function F. Let N*(1) = N(T + t) - N(7) denote the number of events that occur in the first t time units of observation (a) Does the process {N*(?), t> 0} possess independent increments? (b) Repeat (a) when {N(t), t 2 0} is a Poisson process.
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