Hey can someone help? I just can't resolve this problem !

• February 2nd 2010, 06:18 PM
pgl1990
Hey 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 ! :)
• February 2nd 2010, 06:23 PM
matheagle
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 $F_Y(y)=P(Y\le y)=P(\ln X\le y)=P(X\le e^y)=F_X(e^y)$
• February 2nd 2010, 06:26 PM
pgl1990
What I did until now was
P(lnx<y)=P(x<e^y)
and then I was stuck
• February 2nd 2010, 06:29 PM
matheagle
Quote:

Originally Posted by pgl1990
What I did until now was
P(lnx<y)=P(x<e^y)
and then I was stuck

WRITE down your density of X.
I need to know how you write YOUR exponential.
IT makes a diference, one is the reciprocal of the other.
• February 2nd 2010, 06:32 PM
pgl1990
I found exactly the same thing as you in your previous post ( after a few steps)...