5. The continuous random variable \(X\) has the following cumulative distribution function: $$\mathrm { F } ( x ) = \begin{cases} 0 , & x < 0
\frac { 1 } { 432 } x ^ { 2 } \left( x ^ { 2 } - 16 x + 72 \right) , & 0 \leq x \leq 6
1 , & x > 6 \end{cases}$$

1. Find \(\mathrm { P } ( X < 2 )\).
2. Find and specify fully the probability density function \(\mathrm { f } ( x )\) of \(X\).
3. Show that the mode of \(X\) is 2 .
4. State, with a reason, whether the median of \(X\) is higher or lower than the mode of \(X\).