continuous random variable

**ulysses123** · Sep 4th 2010, 11:25 PM

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

**CaptainBlack** · Sep 5th 2010, 01:38 AM

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:

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

and now differentiate wrt $y$ .

CB

**ulysses123** · Sep 5th 2010, 02:22 AM

the cdf gives the probability P(X<x) for some x , why do you have a greater than sighn?

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