continuous random variable

• September 4th 2010, 11:25 PM
ulysses123
continuous random variable
For a positive continuous random variable X, write down the PDF of Y = X² in terms
of the PDF of X
• September 5th 2010, 01:38 AM
CaptainBlack
Quote:

Originally Posted by ulysses123
For a positive continuous random variable X, write down the PDF of Y = X² in terms
of the PDF of X

Let the CDF of $X$ be $F(x)$and that of $Y$ be $G(y)$. Then:

$
G(y)=P(Y>y)=P(Y>x^2)=P(X>\sqrt{y})=F(\sqrt{y})$

and now differentiate wrt $y$.

CB
• September 5th 2010, 02:22 AM
ulysses123
the cdf gives the probability P(X<x) for some x , why do you have a greater than sighn?