2. A bag contains a large number of counters. Each counter has a single digit number on it and the mean of all the numbers in the bag is the unknown parameter \(\mu\). The number 2 is on \(40 \%\) of the counters and the number 5 is on \(25 \%\) of the counters. All the remaining counters have numbers greater than 5 on them. A random sample of 10 counters is taken from the bag.

1. State whether or not each of the following is a statistic
   1. \(S =\) the sum of the numbers on the counters in the sample,
   2. \(D =\) the difference between the highest number in the sample and \(\mu\),
   3. \(F =\) the number of counters in the sample with a number 5 on them. The random variable \(T\) represents the number of counters in a random sample of 10 with the number 2 on them.
2. Specify the sampling distribution of \(T\). The counters are selected one by one.
3. Find the probability that the third counter selected is the first counter with the number 2 on it.