2 Two fair six-sided dice are thrown. The random variable \(X\) denotes the difference between the scores on the two dice. The table shows the probability distribution of \(X\).
| \(r\) | 0 | 1 | 2 | 3 | 4 | 5 |
| \(\mathrm { P } ( X = r )\) | \(\frac { 1 } { 6 }\) | \(\frac { 5 } { 18 }\) | \(\frac { 2 } { 9 }\) | \(\frac { 1 } { 6 }\) | \(\frac { 1 } { 9 }\) | \(\frac { 1 } { 18 }\) |
- Draw a vertical line chart to illustrate the probability distribution.
- Use a probability argument to show that
(A) \(\mathrm { P } ( X = 1 ) = \frac { 5 } { 18 }\),
(B) \(\mathrm { P } ( X = 0 ) = \frac { 1 } { 6 }\). - Find the mean value of \(X\).