(i) The possible scores on the die are 1, 2, 3, and 4. The corresponding areas A are 1, 4, 9, and 16. The probability distribution is:

(ii) To find the expected value E(A), calculate:

\(E(A) = 1 \times \frac{1}{2} + 4 \times \frac{1}{6} + 9 \times \frac{1}{6} + 16 \times \frac{1}{6} = 5.33.\)

To find the variance Var(A), calculate:

\(Var(A) = (1^2 \times \frac{1}{2} + 4^2 \times \frac{1}{6} + 9^2 \times \frac{1}{6} + 16^2 \times \frac{1}{6}) - (5.33)^2 = 30.9.\)