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

$$f ( x ) = \begin{cases} 0.1 x & 0 \leqslant x < 2
k x ( 8 - x ) & 2 \leqslant x < 4
a & 4 \leqslant x < 6
0 & \text { otherwise } \end{cases}$$ where \(k\) and \(a\) are constants.
It is known that \(\mathrm { P } ( X < 4 ) = \frac { 31 } { 45 }\)

1. Find the exact value of \(k\)
2. 1. Find the exact value of \(a\)
   2. Find the exact value of \(\mathrm { P } ( 0 \leqslant X \leqslant 5.5 )\)
3. Specify fully the cumulative distribution function of \(X\)