Adevice contains two circuits. the second circuit is a backup for the first, so the second is used only when the first has failed. the device fails when and only when the second circuit fails. let x and y be the times (in years) at which the first and second circuits fail, respectively. their joint probability density function (pdf) is 6e-xe-20 for 0 < x < y 〈 oo; otherwise (a) find the pdf of x. identify the distribution of x (b) find the pdf of y (c) what is the expected time at which the device fails?

Step-by-step explanation:

The pdf of X is given by 3e^x(1-e^-2y). Please check the screenshot for the workings.

The pdf of Y is given by 6e^-2y. Please check the screenshot for the workings.

The expected time the device fails is the expected time Y fails, so we are going to find the expected time of Y which equals to 0.83.

Please check the screenshop for the workings. Thanks

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