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Thread: Calculating a probability from a pdf.

  1. #1
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    Calculating a probability from a pdf.

    Need help with a question guys, any help will be most appreciated.

    The age of a machine, x, in years, is related to the probability of breakdown, y, by the formula:


    x = 3 + ln(y/1-y)

    Determine the probability of breakdown for 1, 3 and 10 years.

    Where do I start with this one?


    It has got me a bit stumped guys so any help would be most appreciated.

    Thanks
    Last edited by mr fantastic; Dec 20th 2010 at 12:06 PM. Reason: Moved from another thread.
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  2. #2
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    The age of a machine, x, in years, is related to the probability of breakdown, y, by the formula:


    x = 3 + ln(y/1-y)

    Determine the probability of breakdown for 1, 3 and 10 years.
    For example, $\displaystyle 10=3+\ln(y/(1-y))$; we need to find y. Then $\displaystyle \ln(y/(1-y))=7$. Raise $\displaystyle e$ to both sides keeping in mind that $\displaystyle e^{\ln a}=a$ for all $\displaystyle a>0$. This will give you a linear equation on y. Formally, after finding y, you must check that $\displaystyle y/(1-y) > 0$ to make sure that $\displaystyle \ln(y/(1-y))$ exists because when one raises e to both sides of an equation, one can acquire spurious roots.
    Last edited by mr fantastic; Dec 20th 2010 at 12:03 PM.
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