Answer by Xi'an for How do you get the double sum or integral from $E(X+Y)$...
The question of double versus simple sum is mostly a matter of mathematical simplicity.First, as pointed by Stubborn Atom, the question is related with the so-poorly-called "Law of the Unconscious...
View ArticleAnswer by J.C.Wahl for How do you get the double sum or integral from...
If you assume a joint density $p(x,y)$ for $X$ and $Y$ (I have not said anything about the dependency between $X$ and $Y$ here, they can be correlated). The definition of $E(X+Y)$ is:$$E(X + Y) =...
View ArticleHow do you get the double sum or integral from $E(X+Y)$ (expected value)?
I was given a proof for $E(X+Y)$ = $E(X)+E(Y)$ for cases where both variables are either discrete or continuous:Discrete:$$\begin{align*}E(X+Y)&=\sum_{x\in\mathcal X}\sum_{y\in\mathcal...
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