6. A continuous random variable \(X\) has probability density function \(\mathrm { f } ( x )\) where $$f ( x ) = \begin{cases} k \left( 4 x - x ^ { 3 } \right) , & 0 \leqslant x \leqslant 2
0 , & \text { otherwise } \end{cases}$$ where \(k\) is a positive integer.

1. Show that \(k = \frac { 1 } { 4 }\). Find
2. \(\mathrm { E } ( X )\),
3. the mode of \(X\),
4. the median of \(X\).
5. Comment on the skewness of the distribution.
6. Sketch f(x).