4. A continuous random variable \(X\) has cumulative distribution function \(\mathrm { F } ( x )\) given by $$\mathrm { F } ( x ) = \left\{ \begin{array} { c c } 0 & x < 2
k \left( a x + b x ^ { 2 } - x ^ { 3 } \right) & 2 \leqslant x \leqslant 3
1 & x > 3 \end{array} \right.$$ Given that the mode of \(X\) is \(\frac { 8 } { 3 }\)

1. show that \(b = 8\)
2. find the value of \(k\).