Solution Found!
A device contains three components, each of which has a
Chapter 5, Problem 13E(choose chapter or problem)
A device contains three components, each of which has a lifetime in hours with the pdf
\(f(x)=\frac{2 x}{10^{2}} e^{-(x / 10)^{2}}, \quad 0<x<\infty\).
The device fails with the failure of one of the components. Assuming independent lifetimes, what is the probability that the device fails in the first hour of its operation? Hint: \(G(y)=P(Y \leq y)=1-P(Y>y)=1-P\) (all three \(>y\) ).
Equation Transcription:
Text Transcription:
f(x)=2x/10^2e^-(x/10)^2, 0<x<infinity
G(y)=P(Y< or =y)=1-P(Y>y)=1-P
>y
Questions & Answers
QUESTION:
A device contains three components, each of which has a lifetime in hours with the pdf
\(f(x)=\frac{2 x}{10^{2}} e^{-(x / 10)^{2}}, \quad 0<x<\infty\).
The device fails with the failure of one of the components. Assuming independent lifetimes, what is the probability that the device fails in the first hour of its operation? Hint: \(G(y)=P(Y \leq y)=1-P(Y>y)=1-P\) (all three \(>y\) ).
Equation Transcription:
Text Transcription:
f(x)=2x/10^2e^-(x/10)^2, 0<x<infinity
G(y)=P(Y< or =y)=1-P(Y>y)=1-P
>y
ANSWER:
Step 1 of 3
Given
