2022 VJC P2 Q7

An unbiased yellow cubical die has two faces labelled \(10\), two faces labelled \(30\) and two faces labelled \(50\). An unbiased green cubical die has four faces labelled \(60\), one face labelled \(80\) and one face labelled \(100\).

1. When both dice are thrown, the random variable \(X\) is half of the difference between the score on the green die and the score on the yellow die. Find \(\mathrm{E}\left( X \right)\) and \(\mathrm{Var}\left( X \right)\).[4]
2. Suppose now the yellow die is replaced by an unbiased blue cubical die with two faces labelled \(15\), two faces labelled \(35\) and two faces labelled \(55\). The random variable \(W\) is half of the difference between the score on the green die and the score on the blue die. Without doing further calculation, comment on \(\mathrm{E}\left( W \right)\) and \(\mathrm{Var}\left( W \right)\) in relation to \(\mathrm{E}\left( X \right)\) and \(\mathrm{Var}\left( X \right)\) respectively.[2]