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.

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Chapter1: Combinatorial Analysis
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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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