- The continuous random variable \(X\) has the following cumulative distribution function:
$$F ( x ) = \begin{cases} 0 , & x < 2
k \left( 19 x - x ^ { 2 } - 34 \right) , & 2 \leq x \leq 5
1 , & x > 5 \end{cases}$$
- Show that \(k = \frac { 1 } { 36 }\).
- Find \(\mathrm { P } ( X > 4 )\).
- Find and specify fully the probability density function \(\mathrm { f } ( x )\) of \(X\).