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Old November 6th, 2009, 06:39 AM
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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 07:06 AM.
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  #2  
Old November 6th, 2009, 12:12 PM
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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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Old November 6th, 2009, 01:35 PM
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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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