1 In her purse, Katharine has two \(\pounds 5\) notes, two \(\pounds 10\) notes and one \(\pounds 20\) note. She decides to select two of these notes at random to donate to a charity. The total value of these two notes is denoted by the random variable \(\pounds X\).
- (A) Show that \(\mathrm { P } ( X = 10 ) = 0.1\).
(B) Show that \(\mathrm { P } ( X = 30 ) = 0.2\).
The table shows the probability distribution of \(X\).
| \(r\) | 10 | 15 | 20 | 25 | 30 |
| \(\mathrm { P } ( X = r )\) | 0.1 | 0.4 | 0.1 | 0.2 | 0.2 |
- Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).