I have an hard time to understand several things I see on the expectation of two random variables.
First, here is my definition of product of two real valued random variables $X$ and $Y$ defined on the same probability space $(\Omega,\mathcal{A},\mathbb{P})$ :
$$ \mathbb{E}(XY) =\int_{\Omega}X(\omega)Y(\omega)d\mathbb{P} $$
But a lot of time I see double integrals appear when talking about this and I don’t see from where it comes.
Please if you have some insight tl provide don’t hésitate. A question like this has already been askeb but the answer did not help me.
Thank you a lot !