How to compute the expected value of one random variable over sum of iid random variable

Question

If $X_1,\ldots,X_n$ are independent identically distributed positive random variables, prove that $E(\frac{X_i}{X_1+\cdots+X_n})=\frac{1}{n}$, $i=1,\ldots,n$. Can someone give me a hint?

Answer 1

$$ \operatorname{E}\left(\frac{X_1}{X_1+\cdots+X_n}\right) = \cdots = \operatorname{E}\left(\frac{X_n}{X_1+\cdots+X_n}\right) $$ and \begin{align} & \operatorname{E}\left(\frac{X_1}{X_1+\cdots+X_n}\right) + \cdots + \operatorname{E}\left(\frac{X_n}{X_n+\cdots+X_n}\right) \\[10pt] = {} & \operatorname{E}\left(\frac{X_1+\cdots+X_n}{X_1+\cdots+X_n}\right) = \operatorname{E}(1) = 1. \end{align}