Conditional expectation of random variable given a sum – math.stackexchange.com

Let $(X_i)_{i\geq1}$ i.i.d in $\mathcal{L}^1(\Omega,\mathcal{F},p)$ Is it true that $E(X_j|\sum_{i=1}^nX_i)=\frac{1}{n}\sum_{i=1}^nX_i$ For each $j$ where $1\leq j \leq n$. I think it is true, ...

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