The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) = (e-x/1000 )/1000 for x > 0. Determine the probability that:A component lasts more than 1156 hours before failure. Please enter the answer to 3 decimal places.

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Asked Jun 12, 2019
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The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) = (e-x/1000 )/1000 for x > 0. Determine the probability that:

A component lasts more than 1156 hours before failure. Please enter the answer to 3 decimal places.

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Expert Answer

Step 1

Computing the probability that a component lasts more than 1,156 hours before failure:

Define the random variable X as the time to failure of an electronic component in a copier (in hours). The probability density function of the time to failure of an electronic component in a copier is,

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,1,000 f(x)=1000 ; x>0 ;otherwise

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Step 2

A component lasts more than 1,156 hours before failure. That is, the time to failure is...

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P(X 1156) f(x)d 1156 1000 j e dx 1,000 1156 1 1,000 1,156 xp 0001 e100 1,000 1 1,000 156 1,000 1,156 -1,156 1,000 1,000 e -1,156 1,0000 =e -0.3147 Thus, the probability that 0.315 component lasts more than 1,156 hours before failure is a

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