A batch of 1M RAM chips are purchased from two different semiconductorhouses. Let X and

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QUESTION:

A batch of 1M RAM chips are purchased from two different semiconductorhouses. Let X and Y denote the times to failure of the chips purchased fromthe two suppliers. The joint probability density of X and Y is estimated byf(x, y) = e(x+y), x> 0,y> 0,0, otherwise.Assume = 105 per hour and = 106 per hour.Determine the probability that the time to failure is greater for chips character-ized by X than it is for chips characterized by Y .

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QUESTION:

A batch of 1M RAM chips are purchased from two different semiconductorhouses. Let X and Y denote the times to failure of the chips purchased fromthe two suppliers. The joint probability density of X and Y is estimated byf(x, y) = e(x+y), x> 0,y> 0,0, otherwise.Assume = 105 per hour and = 106 per hour.Determine the probability that the time to failure is greater for chips character-ized by X than it is for chips characterized by Y .

ANSWER:

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Given  f(x, y)=

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