7. The continuous random variable \(X\) has cumulative distribution function
$$\mathrm { F } ( x ) = \begin{cases} 0 , & x < 0
2 x ^ { 2 } - x ^ { 3 } , & 0 \leqslant x \leqslant 1
1 , & x > 1 \end{cases}$$
- Find \(\mathrm { P } ( X > 0.3 )\).
- Verify that the median value of \(X\) lies between \(x = 0.59\) and \(x = 0.60\).
- Find the probability density function \(\mathrm { f } ( x )\).
- Evaluate \(\mathrm { E } ( X )\).
- Find the mode of \(X\).
- Comment on the skewness of \(X\). Justify your answer.