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Math Help - There's this proof regarding conditional probability and exponential distributions...

  1. #1
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    Lightbulb There's this proof regarding conditional probability and exponential distributions...

    I finished this proof, but the last line where it says that P(X>y). where does this logic come from?

    Last edited by Statsnoob2718; November 6th 2009 at 06:06 AM.
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  2. #2
    Moo
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    Hello,

    Because \frac{e^{-(x+y)/\theta}}{e^{-x/\theta}}=e^{-y/\theta}
    and we know that for an exponential distribution, the cdf is P(Y\leq y)=1-e^{-y/\theta}

    hence the result
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  3. #3
    MHF Contributor matheagle's Avatar
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    Small x and small y are just constants, X is the rv.

    You had P(X>x) in the denominator on the line above, just replace x with y and you are done.
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