# What will be the pdf of $X+Y$?

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.

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