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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)
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(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)
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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