Here is a cdf for some nonnegative random variable \(X\):

\[ F(x) = \begin{cases} 1-\exp(-\sqrt[3]{x}) & x\geq 0 \\ 0 & \text{else}. \end{cases} \]

1. What is \(P(1 < X <8)\)?
2. What is the pdf of \(X\)?
3. Compute \(E(X^n)\) for any \(n\in\mathbb{N}\).
4. What is the variance of \(X\)?