1. Let N be a Poisson process with intensity λ, with N = {N(t) : t ≥ 0} where N(t) denotes the number of arrivals in the interval (0, t]. Let To, T₁,... be given by To = 0, Tn = inf{t : N(t)=n}. Define the interarrival times X₁, X₂,... by XnTnTn-1 Show that the random variables X₁, X2,... are independent and each have exponential distribution with parameter \.

1. Let N be a Poisson process with intensity λ, with N = {N(t) : t ≥ 0} where N(t) denotes the number of arrivals in the interval (0, t]. Let To, T₁,... be given by To = 0, Tn = inf{t : N(t)=n}. Define the interarrival times X₁, X₂,... by XnTnTn-1 Show that the random variables X₁, X2,... are independent and each have exponential distribution with parameter \.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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