7 The random variable \(X\) has probability density function f given by
$$f ( x ) = \begin{cases} \frac { 1 } { 6 } x & 2 \leqslant x \leqslant 4
0 & \text { otherwise } \end{cases}$$
- Find the distribution function of \(X\).
The random variable \(Y\) is defined by \(Y = X ^ { 3 }\). Find
- the probability density function of \(Y\),
- the value of \(k\) for which \(\mathrm { P } ( Y \geqslant k ) = \frac { 7 } { 12 }\).