5 A discrete random variable \(X\) has the probability distribution $$\mathrm { P } ( X = x ) = \left\{ \begin{array} { c l } \frac { x } { 20 } & x = 1,2,3,4,5
\frac { x } { 24 } & x = 6
0 & \text { otherwise } \end{array} \right.$$

1. Calculate \(\mathrm { P } ( X \geqslant 5 )\).
2. 1. Show that \(\mathrm { E } \left( \frac { 1 } { X } \right) = \frac { 7 } { 24 }\).
   2. Hence, or otherwise, show that \(\operatorname { Var } \left( \frac { 1 } { X } \right) = 0.036\), correct to three decimal places.
3. Calculate the mean and the variance of \(A\), the area of rectangles having sides of length \(X + 3\) and \(\frac { 1 } { X }\).