Question

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 the number of hours at which 12% of all components have failed. Please enter the answer to 2 decimal places.

Step 1

The time to failure of an electronic component in copier follows Exponential Distribution with pdf f(x) = (e^{-x/1000})/1000 for x > 0.

We need to find the value of *x* (number of hours) at which 12% of all component have failed.

Step 2

We have the pdf of exponential distribution but as per the question we need to find the probability that in x hours all components will fail that means we need a cumulative probability till point x.

So, we ...

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