Let {N(t),t e [0, 00)} be a Poisson process with rate A, and X1 be its first arrival time. Show that given N(t) = 1, then X1 is uniformly distributed in (0, t). That is, show that: %3D P(X1 < x|N(t) = 1) = 0
Let {N(t),t e [0, 00)} be a Poisson process with rate A, and X1 be its first arrival time. Show that given N(t) = 1, then X1 is uniformly distributed in (0, t). That is, show that: %3D P(X1 < x|N(t) = 1) = 0
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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Transcribed Image Text:Let {N(t),t e [0, 00)} be a Poisson process with rate A, and X1 be its first
arrival time. Show that given N(t) = 1, then X1 is uniformly distributed in
(0, t). That is, show that:
P(X1 < x|N(t) = 1) = ;
0 < a <t
(3)
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