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b. Use a result from class to find the distribution of the minimum of n independent exponential

b. Use a result from class to find the distribution of the minimum of n independent exponential

A First Course in Probability (10th Edition)
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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b. Use a result from class to find the distribution of the minimum of n independent exponential r.v.'s.
Transcribed Image Text:b. Use a result from class to find the distribution of the minimum of n independent exponential r.v.'s.
independent as selecta Minimum of two exponential rv's week 6 Notebook Q) Suppose X - Exp(₁),Y~ Exp(2₂) are independent. What is the distribution of Z= min(X,Y)? idea: Consider the event E.{Z 7€ 3 for +70 Z>t> X>t and Y> € 30 € = {X> ²₁ Y> +3 So P(E)=P(X7E, Y>E) = P(X>E) P (Y>E) (by indep.) 7 - (hite)t 1- Complete diskibal- fet of Z Auswer Fastest to finish Olet -dit e F₂ (t) = P(Z <t) = 1- e-(desest, [Z~ Explaita₂)] (P(EEE) = What to Dry € edf of exp(2+2) f(²)=
Transcribed Image Text:independent as selecta Minimum of two exponential rv's week 6 Notebook Q) Suppose X - Exp(₁),Y~ Exp(2₂) are independent. What is the distribution of Z= min(X,Y)? idea: Consider the event E.{Z 7€ 3 for +70 Z>t> X>t and Y> € 30 € = {X> ²₁ Y> +3 So P(E)=P(X7E, Y>E) = P(X>E) P (Y>E) (by indep.) 7 - (hite)t 1- Complete diskibal- fet of Z Auswer Fastest to finish Olet -dit e F₂ (t) = P(Z <t) = 1- e-(desest, [Z~ Explaita₂)] (P(EEE) = What to Dry € edf of exp(2+2) f(²)=
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