Problem 5 Let N₁ (t) and N₂ (t) be two independent Poisson processes with rate ₁ and >₂ respectively. Let N(t) = N₁ (t) + N₂(t) be the merged process. Show that given N(t) N₁ (t) ~ Binomial (n,₁). = Note: We can interpret this result as follows: Any arrival in the merged process belongs to N₁(t) with probability and belongs to N₂(t) with probability 12 independent of other arrivals. X₁ +d₂ X₁ + λ2
Problem 5 Let N₁ (t) and N₂ (t) be two independent Poisson processes with rate ₁ and >₂ respectively. Let N(t) = N₁ (t) + N₂(t) be the merged process. Show that given N(t) N₁ (t) ~ Binomial (n,₁). = Note: We can interpret this result as follows: Any arrival in the merged process belongs to N₁(t) with probability and belongs to N₂(t) with probability 12 independent of other arrivals. X₁ +d₂ X₁ + λ2
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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