Suppose that \(X\) is a random variable whose density is

\[f(x)=\frac{1}{2(1+|x|)^2} \quad x \in (-\infty,\infty)\]

1. Draw a graph of \(f(x)\).
2. Find \(\mathbf{P}(-1 <X<2)\).
3. Find \(\mathbf{P}(X>1)\).
4. Is \(\mathbf{E}(X) \) defined ? Explain.