Probability Density Function Help

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Homework Help Overview

The discussion revolves around a probability density function related to the time to failure of an electric component. The original poster seeks assistance in determining the probability that a component lasts more than a specified time and how to find the time at which 10% of components have failed.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster indicates understanding of how to calculate the probability for a component lasting more than 1000 hours but expresses uncertainty about the integration limits for finding the time at which 10% of components have failed. Another participant suggests using the cumulative distribution function to find when F(x) equals 0.10.

Discussion Status

The discussion is ongoing, with the original poster acknowledging the suggestion but later indicating that the proposed solution did not yield the expected result. This suggests that further exploration of the problem is needed.

Contextual Notes

The original poster mentions a lack of clarity regarding the integration interval for the second part of the problem, indicating potential confusion about the application of the cumulative distribution function.

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Probability Density Function...Help

The probabiltiy density function of the time to failure of an electric component in hours is f(x)=e^{(-x/3000)/3000} for x > 0 and f(x) = 0 for x \leq 0 determine the probability that

a) A component last more than 1000 hours before failure
I know how to solve this part. All I have to to is integrate the given function from [1000, infinity].

But how do determine the number of hours at which 10% of all the components have failed? I don't know what interval I should integrate over. Any Ideas?
 
Last edited:
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If F(x) is the probability that a component has failed by time x, you are looking for when F(x) = .10. Can you solve that?
 
yes I can. thank you!
 
when I solve it as you state that is no the answer.
any other ideas?
 

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