An engineer designs a circuit, seen below. In this system, if the first component fails, the functionality moves immediately to the second component and so on. The system only fails when the fifth component fails. Each component has a lifetime that is exponentially distribut with λ = 0.01 and components fail independently of one another. Define A, to be the length time component į lasts. Let Y = the time at which the new system fails.

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An engineer designs a circuit, seen below. In this system, if the first component fails, the
functionality moves immediately to the second component and so on. The system only fails
when the fifth component fails. Each component has a lifetime that is exponentially distributed
with λ = 0.01 and components fail independently of one another. Define A, to be the length of
time component i lasts. Let Y = the time at which the new system fails.
Given
2
3
5
A-Exponential (0.01)
• Y=A1+A2+A3+A4+A5
1. What is the expected lifetime of this new system?
Transcribed Image Text:An engineer designs a circuit, seen below. In this system, if the first component fails, the functionality moves immediately to the second component and so on. The system only fails when the fifth component fails. Each component has a lifetime that is exponentially distributed with λ = 0.01 and components fail independently of one another. Define A, to be the length of time component i lasts. Let Y = the time at which the new system fails. Given 2 3 5 A-Exponential (0.01) • Y=A1+A2+A3+A4+A5 1. What is the expected lifetime of this new system?
Expert Solution
Step 1

Given:

Ai ~ Exp λ=0.01

Y= A1 + A2 + A3 + A4 + A5

 

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