題組內容

3. Let \( X \) and \( Y \) be random variables and \( \{X_n, n \ge 1\} \) be a sequence of random variables. Define \[ \rho(X) = E\left( \frac{|X|}{1+|X|} \right). \] Show that


(a) $\rho(X + Y) \le \rho(X) + \rho(Y)$, (5%)