7. The random variable \(X\) has probability distribution
| \(x\) | 1 | 3 | 5 | 7 | 9 |
| \(\mathrm { P } ( X = x )\) | 0.2 | \(p\) | 0.2 | \(q\) | 0.15 |
- Given that \(\mathrm { E } ( X ) = 4.5\), write down two equations involving \(p\) and \(q\).
Find
- the value of \(p\) and the value of \(q\),
- \(\mathrm { P } ( 4 < X \leqslant 7 )\).
Given that \(\mathrm { E } \left( X ^ { 2 } \right) = 27.4\), find
- \(\operatorname { Var } ( X )\),
- \(\mathrm { E } ( 19 - 4 X )\),
- \(\operatorname { Var } ( 19 - 4 X )\).