3 The probability distribution of a random variable \(X\) is shown.
| \(x\) | 1 | 3 | 5 | 7 |
| \(\mathrm { P } ( X = x )\) | 0.4 | 0.3 | 0.2 | 0.1 |
- Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).
- Three independent values of \(X\), denoted by \(X _ { 1 } , X _ { 2 }\) and \(X _ { 3 }\), are chosen. Given that \(X _ { 1 } + X _ { 2 } + X _ { 3 } = 19\), write down all the possible sets of values for \(X _ { 1 } , X _ { 2 }\) and \(X _ { 3 }\) and hence find \(\mathrm { P } \left( X _ { 1 } = 7 \right)\).
- 11 independent values of \(X\) are chosen. Use an appropriate formula to find the probability that exactly 4 of these values are 5 s .