(i) The possible values of \(X\) are 0, 1, and 2. The probability distribution is:

(ii) To find \(E(X)\), use the formula:

\(E(X) = \sum x P(X = x) = 0 \times \frac{1}{7} + 1 \times \frac{4}{7} + 2 \times \frac{2}{7} = \frac{8}{7}\).

To find \(\text{Var}(X)\), use the formula:

\(\text{Var}(X) = E(X^2) - (E(X))^2\).

First, calculate \(E(X^2)\):

\(E(X^2) = 0^2 \times \frac{1}{7} + 1^2 \times \frac{4}{7} + 2^2 \times \frac{2}{7} = \frac{12}{7}\).

Then, \(\text{Var}(X) = \frac{12}{7} - \left(\frac{8}{7}\right)^2 = \frac{12}{7} - \frac{64}{49} = \frac{20}{49}\).