6 The continuous random variable \(X\) has probability density function f given by
$$\mathrm { f } ( x ) = \begin{cases} 0 & x < 1
\frac { 1 } { 2 } & 1 \leqslant x \leqslant 3
0 & x > 3 \end{cases}$$
Find the distribution function of \(X\).
The random variable \(Y\) is defined by \(Y = X ^ { 3 }\). Find
- the probability density function of \(Y\),
- the expected value and variance of \(Y\).