6 The continuous random variable \(X\) has probability density function f given by $$f ( x ) = \begin{cases} \frac { 1 } { 8 } & 0 \leqslant x < 1
\frac { 1 } { 28 } ( 8 - x ) & 1 \leqslant x \leqslant 8
0 & \text { otherwise } \end{cases}$$

1. Find the cumulative distribution function of \(X\).
2. Find the value of the constant \(a\) such that \(\mathrm { P } ( \mathrm { X } \leqslant \mathrm { a } ) = \frac { 5 } { 7 }\).
   The random variable \(Y\) is given by \(Y = \sqrt [ 3 ] { X }\).
3. Find the probability density function of \(Y\).
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.