I have obtained the pdf and its distribution seems to be a triangle. Now, I want to take the square of this pdf like
${f_Y(y)}^2$
How can I obtain the square of this pdf?
Do, I just need to simply multiply the two $f_Y(y)$?
I have obtained the pdf and its distribution seems to be a triangle. Now, I want to take the square of this pdf like
${f_Y(y)}^2$
How can I obtain the square of this pdf?
Do, I just need to simply multiply the two $f_Y(y)$?
If $f(x)$ is the pdf of $X$, then $f(x)^2$ is NOT the pdf of $X^2$. Write $F(x)$ as the cdf of $X$: $F(x)=P(X\leq x)$. Then if $G$ is the cdf of $Y:=X^2$, $G(y):=P(Y\leq y)=P(x^2\leq y)=P(-\sqrt{y}\leq x\leq \sqrt{y})$, and assuming $X$ has a continuous cdf, $G(y)=F(\sqrt{y})-F(-\sqrt{y})$, which gives $g(y)=G'(y)=\frac{1}{2\sqrt{y}}(f(\sqrt{y})+f(-\sqrt{y}))$