Let (x(t)) be a Poisson process with rate A, and let T₁ = min{t: X(t) > 1} bethe first arrival time. Prove that T₁ is exponentially distributed with rate \.

The first arrival time ( T1) in a Poisson process with rate (λ) is exponentially distributed with…

Answered: Let (x(t)) be a Poisson process with…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Let (x(t)) be a Poisson process with rate A, and let T₁ = min{t: X(t) > 1} be the first arrival time. Prove that T₁ is exponentially distributed with rate \.