If X has an exponential distribution with the parameter θ, use the distribution function technique to find the probability density of the random variable Y=ln(x) .

Thank you for any help ! :)

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- Feb 2nd 2010, 05:18 PMpgl1990Hey can someone help? I just can't resolve this problem !
If X has an exponential distribution with the parameter θ, use the distribution function technique to find the probability density of the random variable Y=ln(x) .

Thank you for any help ! :) - Feb 2nd 2010, 05:23 PMmatheagle
FIRST of all you need to write down your exponential density.

There are two ways of writing it, so you need to be clear.

Then find the cdf and substitute the new rv.

For example $\displaystyle F_Y(y)=P(Y\le y)=P(\ln X\le y)=P(X\le e^y)=F_X(e^y)$ - Feb 2nd 2010, 05:26 PMpgl1990
What I did until now was

P(lnx<y)=P(x<e^y)

and then I was stuck - Feb 2nd 2010, 05:29 PMmatheagle
- Feb 2nd 2010, 05:32 PMpgl1990
I found exactly the same thing as you in your previous post ( after a few steps)...