Consider a nonnegative, absolutely continuous random variable with cdf

\[ F_X(x) = \begin{cases} 1 - \exp\left(-\frac{x^2}{2}\right) & x\geq 0 \\ 0 & x<0. \end{cases} \]

1. What is \(P(2\leq X\leq 3)\);
2. What is the density of \(X\)?
3. What is \(E(X^n)\) for any \(n\in\mathbb{N}\)?
4. What is \(\text{var}(X)\)?
5. What is the median of \(X\)?