1. theoretical exercises about probability problems

Let X1,...,Xn be independent and identically distributed random variables. Find

E[X1|X1+...+Xn=x]

2. Re: theoretical exercises about probability problems

I believe it will be
$\dfrac{x}{n}$

3. Re: theoretical exercises about probability problems

$\displaystyle \sum_{k=1}^n~E[X_k | X_1 + \dots +X_n = x] = x$

$E[X_1 | X_k + \dots +X_n = x] = E[X_k | X_1 + \dots +X_n = x],~\forall k \in [1,n]$

Thus

$E[X_1 | X_k + \dots +X_n = x] = \dfrac x n$