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Solving PDF with set boundary values

  1. Oct 13, 2012 #1
    I am give probability distribution function f(x)=(e(-x/1000))/1000 of the time to failure of an electronic component in a copier

    The question is to determine the number of hours at which 10% of all components have failed.

    My solution:
    1) PDF was integrated to obtain: f(x)= e(-x/1000)

    2) Then, I used e(-x/1000)=0.1 with upper boundary x, and lower boundary is 0 to find x as the number of hours at which all 10% of components have failed. However, entering it in calculator, I couldn't obtain solution. What did I wrong here?
  2. jcsd
  3. Oct 13, 2012 #2

    Stephen Tashi

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    Science Advisor

    You're using "f(x)" inconsistently to stand for two different things and your antiderivative is missing a negative sign.

    [itex] \int \frac{e^{-x/1000}}{1000} dx = - e^{-x/1000} + C [/itex]

    You can't compute a deterministic answer for the time when 10% of the components have failed since that time is a random variable. Perhaps you want to compute the time at which the probability that a component has failed then or earlier reaches .10. Your description of what you did with the calculator isn't clear.
  4. Oct 14, 2012 #3
    Ein Krieger,

    I am pretty sure you are leaving out one critical part of the definition of f(x). The pdf is

    [tex]f(x) =\frac{1}{1000} e^{-x / 1000}[/tex]
    for [itex]x \ge 0[/itex], zero otherwise.

    So you should integrate f(x) from 0 to x; you will get a different answer for the cdf than you got before.
  5. Oct 14, 2012 #4
    Yes. Sure. You are right. Time is continuous variable so it is inconsistent to try to define exact probability. All we need is to get probability for time range.

    I have already calculated, and I got 105 hours. is it right?
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