Suppose X₁, X2, ···, , Xn are independent exponential (A) variables. Show that Xn Y = min{X₁, X2, ..., Xn} is exponential(nλ).

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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Suppose X₁, X2,..., Xn are independent exponential (A) variables. Show that
Y = min{X₁, X₂,
‚Xn}
is exponential(nλ).
Transcribed Image Text:Suppose X₁, X2,..., Xn are independent exponential (A) variables. Show that Y = min{X₁, X₂, ‚Xn} is exponential(nλ).
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