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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