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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.

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It is called convolution

$h(x) = \int_{-\infty} ^ {\infty} f(y) g(x-y) dy $

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