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Mathematics, 11.03.2020 04:34 blachaze8729

A production facility contains two machines that are used to reworkitems that are initially defective.

LetXbe the number of hours that the firstmachine is in use, and letYbe the number of hours that the second machine isin use, on a randomly chosen day.

Assume that X and Y have joint probabilitydensity function given by, f(x, y) ={32(x2+y2)0< x <1 and 0< y <10 otherwise

What is the probability that both machines are in operation for more than half an hour?

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