1. A continuous random variable \(X\) has probability density function

$$f ( x ) = \left\{ \begin{array} { c c } \frac { x } { 16 } \left( 9 - x ^ { 2 } \right) & 1 \leqslant x \leqslant 3
0 & \text { otherwise } \end{array} \right.$$

1. Find the cumulative distribution function of \(X\)
2. Calculate \(\mathrm { P } ( X > 1.8 )\)
3. Use calculus to find \(\mathrm { E } \left( \frac { 3 } { X } + 2 \right)\)
4. Show that the mode of \(X\) is \(\sqrt { 3 }\)