4 A fair 8 -sided dice has faces labelled \(1,2 , \ldots , 8\). The random variable \(X\) represents the score when the dice is rolled once.
- State the distribution of \(X\).
- Find \(\mathrm { P } ( X < 4 )\).
- Find each of the following.
- \(\mathrm { E } ( X )\)
- \(\operatorname { Var } ( X )\)
- The random variable \(Y\) is defined by \(Y = 10 X + 5\). Find each of the following.
- \(\mathrm { E } ( Y )\)
- \(\operatorname { Var } ( Y )\)