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%)