9 The table shows the probability distribution for the discrete random variable \(X\).
| \(x\) | 1 | 2 | 3 | 4 | 5 |
| \(\mathrm { P } ( \mathrm { X } = \mathrm { x } )\) | 0.1 | 0.3 | \(q\) | \(2 q\) | \(3 q\) |
You are given that \(q\) is a positive constant.
- Determine the value of \(q\).
- Calculate \(\mathrm { P } ( X \leqslant 4 )\).
Two independent values of \(X\) are taken.
- Determine the probability that the sum of the two values is 3 .
Fifty independent values of \(X\) are taken.
- Find the probability that a value of 2 occurs exactly 17 times.