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
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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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)=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ce6fdd3-7319-4b16-8948-2d2b1b56e05e%2F0488e66b-3599-427e-888a-e841b6b68290%2Fizywosa_processed.png&w=3840&q=75)
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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