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

• November 6th 2009, 04:39 AM
Statsnoob2718
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?

http://i33.tinypic.com/2iqlvk7.jpg
• November 6th 2009, 10:12 AM
Moo
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
• November 6th 2009, 11:35 AM
matheagle
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.