4. A six-sided die is biased such that there is an equal chance of scoring each of the numbers from 1 to 5 but a score of 6 is three times more likely than each of the other numbers.

1. Write down the probability distribution for the random variable, \(X\), the score on a single throw of the die.
2. Show that \(\mathrm { E } ( X ) = \frac { 33 } { 8 }\).
3. Find \(\mathrm { E } ( 4 X - 1 )\).
4. Find \(\operatorname { Var } ( X )\).