1 Ryan has 6 one-pound coins and 4 two-pound coins. Ryan decides to select 3 of these coins at random to donate to a charity. The total value, in pounds, of these 3 coins is denoted by the random variable \(X\).

1. Show that \(\mathrm { P } ( X = 3 ) = \frac { 1 } { 6 }\). The table below shows the probability distribution of \(X\).

   \(r\)	3	4	5	6
   \(\mathrm { P } ( \mathrm { X } = \mathrm { r } )\)	\(\frac { 1 } { 6 }\)	\(\frac { 1 } { 2 }\)	\(\frac { 3 } { 10 }\)	\(\frac { 1 } { 30 }\)

2. Draw a graph to illustrate the distribution.
3. In this question you must show detailed reasoning. Find each of the following.
   • \(\mathrm { E } ( X )\)
   • \(\operatorname { Var } ( X )\)
   Ryan's friend Sasha decides to give the same amount as Ryan does to the charity plus an extra three pounds. The random variable \(Y\) represents the total amount of money, in pounds, given by Ryan and Sasha.
4. Determine each of the following.
   • E (Y)
   • \(\operatorname { Var } ( Y )\)