[See Steps] A device consists of five independent electronic components that perform the same function. Assume the components are connected in parallel
Question: A device consists of five independent electronic components that perform the same function.
- Assume the components are connected in parallel and the time to failure of component \(1 \leq i \leq 5\) is the random variable \(X_{i} \sim \operatorname{EXP}(1) .\) Find the pdf for \(Y\), the device's time to failure.
- Repeat (a) but with the components in series and not in parallel.
- Suppose the device fails when three of the five components fails. Give the pdf of \(Y\), the time to failure of this device.
- What is the average expected increase in device lifespan created by placing the five components in parallel instead of in series?
Deliverable: Word Document 
(See Solution) The random variable X has the pdf: f_X(x)=(1)/(2
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[Solution Library] Find out what jointly Gaussian density is and plot
![[Step-by-Step] Generate independent random variables from two](/images/solutions/MC-solution-library-77081.jpg "[Step-by-Step] Generate independent random variables from two")
[Step-by-Step] Generate independent random variables from two
(See Steps) Consider the following joint probability mass function
![(Solution Library) Show that E[ g(X^2)Y|X ]=g(X^2)E[](/images/solutions/MC-solution-library-77083.jpg "(Solution Library) Show that E[ g(X^2)Y|X ]=g(X^2)E[ Y|X")
(Solution Library) Show that E[ g(X^2)Y|X ]=g(X^2)E[ Y|X
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