7. A random variable \(X\) has probability density function given by $$f ( x ) = \begin{cases} \frac { 1 } { 3 } , & 0 \leq x \leq 1
\frac { 8 x ^ { 3 } } { 45 } , & 1 \leq x \leq 2
0 , & \text { otherwise } \end{cases}$$

1. Calculate the mean of \(X\).
2. Specify fully the cumulative distribution function \(\mathrm { F } ( x )\).
3. Find the median of \(X\).
4. Comment on the skewness of the distribution of \(X\). END