3. The discrete random variable \(X\) has probability function
\(\mathrm { P } ( X = x ) = \begin{cases} k x , & x = 1,2,3,4,5 ,
0 , & \text { otherwise } . \end{cases}\)

1. Show that \(k = \frac { 1 } { 15 }\). Find the value of
2. \(\mathrm { E } ( 2 X + 3 )\),
3. \(\operatorname { Var } ( 2 X - 4 )\).
   (6)