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6.1.1 Let X(t) be a Yule process that is observed at a random time U, where U is uniformly distributed over [0, 1). Show that Pr{X(U) =k}=pk/(ẞk) for k = 1, 2,..., with p=1-e-B

6.1.1 Let X(t) be a Yule process that is observed at a random time U, where U is uniformly distributed over [0, 1). Show that Pr{X(U) =k}=pk/(ẞk) for k = 1, 2,..., with p=1-e-B

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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6.1.1 Let X(t) be a Yule process that is observed at a random time U, where U is uniformly distributed over [0, 1). Show that Pr{X(U) =k}=pk/(ẞk) for k = 1, 2,..., with p=1-e-B
Transcribed Image Text:6.1.1 Let X(t) be a Yule process that is observed at a random time U, where U is uniformly distributed over [0, 1). Show that Pr{X(U) =k}=pk/(ẞk) for k = 1, 2,..., with p=1-e-B
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