5 In a computer game, players try to collect five treasures. The number of treasures that Isaac collects in one play of the game is represented by the discrete random variable \(X\). The probability distribution of \(X\) is defined by $$\mathrm { P } ( X = x ) = \left\{ \begin{array} { c l } \frac { 1 } { x + 2 } & x = 1,2,3,4
k & x = 5
0 & \text { otherwise } \end{array} \right.$$

1. 1. Show that \(k = \frac { 1 } { 20 }\).
   2. Calculate the value of \(\mathrm { E } ( X )\).
   3. Show that \(\operatorname { Var } ( X ) = 1.5275\).
   4. Find the probability that Isaac collects more than 2 treasures.
2. The number of points that Isaac scores for collecting treasures is \(Y\) where $$Y = 100 X - 50$$ Calculate the mean and the standard deviation of \(Y\).