2. The discrete random variable \(X\) can take any value in the set \(\{ 1,2,3,4,5,6,7,8 \}\). Arthur, Beatrice and Chris each carry out trials to investigate the distribution of \(X\). Arthur finds that \(\mathrm { P } ( X = 1 ) = 0.125\) and that \(\mathrm { E } ( X ) = 4.5\).
Beatrice finds that \(\mathrm { P } ( X = 2 ) = \mathrm { P } ( X = 3 ) = \mathrm { P } ( X = 4 ) = p\).
Chris finds that the values of \(X\) greater than 4 are all equally likely, with each having probability \(q\).

1. Calculate the values of \(p\) and \(q\).
2. Give the name for the distribution of \(X\).
3. Calculate the standard deviation of \(X\).