# Thread: Find the pdf

1. ## Find the pdf

Let X be a Uniform(0,1) random variable. Find the pdf of Y = (-1/lamda)*ln(X) , where lamda is a given positive number.

I don't think this is very difficult, but I'm not really sure how to go about it when X and Y are together like that. If anyone could point me in the right direction I'd really appreciate it!

2. Hint -
1. Try plotting y as f(x)? What is the range it takes?
2. Can you find the cdf for y? i.e. Prob (y<y0)
3. Differentiate the cdf to get pdf

This should not be too tough

3. Use Calc 1

$\displaystyle f_Y(y)=f_X(x)\left|{dx\over dy}\right|$

4. Originally Posted by jlt1209
Let X be a Uniform(0,1) random variable. Find the pdf of Y = (-1/lamda)*ln(X) , where lamda is a given positive number.

I don't think this is very difficult, but I'm not really sure how to go about it when X and Y are together like that. If anyone could point me in the right direction I'd really appreciate it!
Originally Posted by matheagle
Use Calc 1

$\displaystyle f_Y(y)=f_X(x)\left|{dx\over dy}\right|$
Alternatively, since X ~ U(0, 1) => 1 - X ~ U(0, 1) it follows immediately from the probability integral transform theorem that Y is an exponential random variable with pdf $\displaystyle \lambda e^{- \lambda y}$.