1 The discrete random variable \(A\) has the following probability distribution.
| \(a\) | 1 | 2 | 5 | 10 | 20 |
| \(\mathrm { P } ( A = a )\) | 0.3 | 0.1 | 0.1 | 0.2 | 0.3 |
- Find the value of \(\mathrm { E } ( A )\).
- Determine the value of \(\operatorname { Var } ( A )\).
- The variable \(A\) represents the value in pence of a coin chosen at random from a pile. Mia picks one coin at random from the pile. She then adds, from a different source, another coin of the same value as the one that she has chosen, and one 50p coin.
- Find the mean of the value of the three coins.
- Find the variance of the value of the three coins.