8. Let $X_1, X_2, \dots, X_n$ be positive, identically distributed random variables. For $1 \le i \le n$, let
$Z_i = \frac{X_i}{X_1 + X_2 + \dots + X_n}$.
Show that $Z_1, Z_2, \dots, Z_n$ are also identically distributed and, for $1 \le i \le n$, find $E(Z_i)$.