Let $X$ and $Y$ be two independent random variables, taking values in $\mathbf{N}$, defined on the same probability space $(\Omega, \mathcal{A}, P)$. Prove the relation $$p_{X+Y} = p_X * p_Y$$
Let $X$ and $Y$ be two independent random variables, taking values in $\mathbf{N}$, defined on the same probability space $(\Omega, \mathcal{A}, P)$. Prove the relation
$$p_{X+Y} = p_X * p_Y$$