2 Gohan throws a fair tetrahedral die with faces numbered \(1,2,3,4\). If she throws an even number then her score is the number thrown. If she throws an odd number then she throws again and her score is the sum of both numbers thrown. Let the random variable \(X\) denote Gohan's score.

1. Show that \(\mathrm { P } ( X = 2 ) = \frac { 5 } { 16 }\).
2. The table below shows the probability distribution of \(X\).

   \(x\)	2	3	4	5	6	7
   \(\mathrm { P } ( X = x )\)	\(\frac { 5 } { 16 }\)	\(\frac { 1 } { 16 }\)	\(\frac { 3 } { 8 }\)	\(\frac { 1 } { 8 }\)	\(\frac { 1 } { 16 }\)	\(\frac { 1 } { 16 }\)

   Calculate \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).