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

http://i33.tinypic.com/2iqlvk7.jpg

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- Nov 6th 2009, 04:39 AMStatsnoob2718There'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?

http://i33.tinypic.com/2iqlvk7.jpg - Nov 6th 2009, 10:12 AMMoo
Hello,

Because $\displaystyle \frac{e^{-(x+y)/\theta}}{e^{-x/\theta}}=e^{-y/\theta}$

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

hence the result - Nov 6th 2009, 11:35 AMmatheagle
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.