Thread: find the probability density function of the random variable Y=lnX

If X is an exponential random variable with parameter , find the probability density function of the random variable Y=lnX.
HINT: Find the cummulative distribution function.

I don't understand what the hint saying, find the cdf of what? when =1, we have , Y=lnX implies , if I sub to f(x), it will be very hard to do the integral, any simple way to do this?

Originally Posted by wopashui

If X is an exponential random variable with parameter , find the probability density function of the random variable Y=lnX.
HINT: Find the cummulative distribution function.

I don't understand what the hint saying, find the cdf of what? when =1, we have , Y=lnX implies , if I sub to f(x), it will be very hard to do the integral, any simple way to do this?

Well, here is a hint for the hint: Research the probability integral transform theorem.

Originally Posted by wopashui

If X is an exponential random variable with parameter , find the probability density function of the random variable Y=lnX.
HINT: Find the cummulative distribution function.

I don't understand what the hint saying, find the cdf of what? when =1, we have , Y=lnX implies , if I sub to f(x), it will be very hard to do the integral, any simple way to do this?

The hint is suggesting you to find:



CB