<p><a href="https://stats.stackexchange.com/questions/184380/mathbbes-n-when-s-n-takes-x-1-x-n-or-y-1-y-n">$\mathbb{E}[S_n]$, when $S_n$ takes $X_1+...+X_n$ or $Y_1+...+Y_n$?</a></p>

<p>I don't think it is the same thing as:</p>

<p><a href="https://stats.stackexchange.com/questions/184189/why-does-mathbbe-fracx-1-x-nn-mathbbex">Why does $\mathbb{E}(\frac{X_1+...+X_n}{n})=\mathbb{E}(X)$?</a></p>

<p>because the former involves conditional expectation.</p>
