Let {N(t), t [0,)} be a Poisson process with rate . Show the following: given that
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Let {N(t), t ∈ [0,∞)} be a Poisson process with rate λ. Show the following: given that N(t) = n, the n arrival times have the same joint CDF as the order statistics of n independent Uniform(0, t) random variables. To show this you can show that
Transcribed Image Text:
n!
fT₁, T2, Tn N(t)-n (t1, t2,..., tn) =
th
3
for 0 < t
n!
fT₁, T2, Tn N(t)-n (t1, t2,..., tn) =
th
3
for 0 < t
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Related Book For
Introduction To Probability Statistics And Random Processes
ISBN: 9780990637202
1st Edition
Authors: Hossein Pishro-Nik
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