A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Y be the number of hours...

A production facility contains two machines that are used to rework items that are initially<br>defective. Let X be the number of hours that the first machine is in use, and let Y be the<br>number of hours that the second machine is in use, on a randomly chosen day.<br>Assume that X and Y have joint probability density function given by<br>(* + y?)<br>0 <x < 1 and 0 < y < 1<br>f(x) =<br>otherwise<br>What is the probability that both machines are in operation for more than half an hour?<br>a.<br>Find the marginal probability density functions fx(x) and fy(y).<br>b.<br>Are X and Y independent? Explain.<br>c.<br>

Extracted text: A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Y be the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint probability density function given by (* + y?) 0 < 1="" and="" 0="">< y="">< 1="" f(x)="otherwise" what="" is="" the="" probability="" that="" both="" machines="" are="" in="" operation="" for="" more="" than="" half="" an="" hour?="" a.="" find="" the="" marginal="" probability="" density="" functions="" fx(x)="" and="" fy(y).="" b.="" are="" x="" and="" y="" independent?="" explain.="">

Jun 02, 2022

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A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Y be the number of hours...

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