6. A continuous random variable \(X\) has cumulative distribution function \(\mathrm { F } ( x )\) given by
$$F ( x ) = \left\{ \begin{array} { l c }
0 & x < 0
\frac { x ^ { 2 } } { 20 } ( 9 - 2 x ) & 0 \leqslant x \leqslant 2
1 & x > 2
\end{array} \right.$$
- Verify that the median of \(X\) lies between 1.23 and 1.24
- Specify fully the probability density function \(\mathrm { f } ( x )\).
- Find the mode of \(X\).
- Describe the skewness of this distribution. Justify your answer.