2. A farmer sells boxes of eggs. The eggs are sold in boxes of 6 eggs and boxes of 12 eggs in the ratio \(n : 1\) A random sample of three boxes is taken.
The number of eggs in the first box is denoted by \(X _ { 1 }\)
The number of eggs in the second box is denoted by \(X _ { 2 }\)
The number of eggs in the third box is denoted by \(X _ { 3 }\)
The random variable \(T = X _ { 1 } + X _ { 2 } + X _ { 3 }\)
Given that \(\mathrm { P } ( T = 18 ) = 0.729\)

1. show that \(n = 9\)
2. find the sampling distribution of \(T\) The random variable \(R\) is the range of \(X _ { 1 } , X _ { 2 } , X _ { 3 }\)
3. Using your answer to part (b), or otherwise, find the sampling distribution of \(R\)