2. The discrete random variable \(X\) has the probability function shown below. $$P ( X = x ) = \left\{ \begin{array} { l c } \frac { k } { x } , & x = 1,2,3,4
0 , & \text { otherwise } . \end{array} \right.$$

1. Show that \(k = \frac { 12 } { 25 }\) Find
2. \(\mathrm { F } ( 2 )\),
3. \(\mathrm { E } ( X )\),
4. \(\mathrm { E } \left( X ^ { 2 } + 2 \right)\).