An absolutely continuous random variable \(X\) has pdf

\[ f(x)=\begin{cases} \frac{3}{22}[5 - (x-1)^2] & 1\leq x \leq3\\ 0 & \text{else}. \end{cases} \]

1. What is the range of \(X\)?
2. Confirm that \(f\) is a valid pdf.
3. Derive the formula for the cdf of \(X\) and plot it.
4. Compute \(P(0.9 < X < 1.1)\).
5. Compute \(E(X)\).
6. Compute \(\text{var}(X)\).