Question: Let {N(t), t 0} be a nonhomogeneous Poisson process with intensity function A(t), t 0 However, suppose one starts observing the process at a random

Let {N(t), t 0} be a nonhomogeneous Poisson process with intensity function A(t), t 0 However, suppose one starts observing the process at a random time 7 having distribution function F. Let N*(t) = N(T + t) N(7) denote the number of events that occur in the first time units of observation

(a) Does the process {N*(t), t 0} possess independent increments?

(b) Repeat

(a) when {N(t), t 0} is a Poisson process.

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