Suppose $X$ and $Y$ are independent random variables. Let $f$ and $g$ be the pdf of $X$ and $Y$ respectively. Let $h$ be the pdf of $X+Y$ then can we say that $h(x)=f(x)g(x),$ for all $x \in \Bbb R$? If so why?
Please help me in this regard. Thank you very much.
It is called convolution
$h(x) = \int_{-\infty} ^ {\infty} f(y) g(x-y) dy $