Thread: continuous random variable

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

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 $\displaystyle X$ be $\displaystyle F(x) $and that of $\displaystyle Y$ be $\displaystyle G(y)$. Then:

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

and now differentiate wrt $\displaystyle y$.

CB

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