5. The discrete random variable \(X\) takes only the values 4, 5, 6, 7, 8 and 9. The probabilities of these values are given in the table:
| \(x\) | 4 | 5 | 6 | 7 | 8 | 9 |
| \(\mathrm { P } ( X = x )\) | \(p\) | 0.1 | \(q\) | \(q\) | 0.3 | 0.2 |
It is known that \(\mathrm { E } ( X ) = 6 \cdot 7\). Find
- the values of \(p\) and \(q\),
- the value of \(a\) for which \(\mathrm { E } ( 2 X + a ) = 0\),
- \(\operatorname { Var } ( X )\).
\section*{STATISTICS 1 (A) TEST PAPER 9 Page 2}