5. A bag contains a large number of counters with \(35 \%\) of the counters having a value of 6 and \(65 \%\) of the counters having a value of 9
A random sample of size 2 is taken from the bag and the value of each counter is recorded as \(X _ { 1 }\) and \(X _ { 2 }\) respectively.
The statistic \(Y\) is calculated using the formula
$$Y = \frac { 2 X _ { 1 } + X _ { 2 } } { 3 }$$
- List all the possible values of \(Y\).
- Find the sampling distribution of \(Y\).
- Find \(\mathrm { E } ( Y )\).