(a) The probability distribution table for X is:

(b) To find E(X), calculate:

E(X) = \frac{1 \times 2 + 4 \times 3 + 10 \times 4 + 12 \times 5 + 9 \times 6}{36} = \frac{2 + 12 + 40 + 60 + 54}{36} = \frac{168}{36} = \frac{14}{3}

To find Var(X), calculate:

\(\text{Var}(X) = \frac{1 \times 2^2 + 4 \times 3^2 + 10 \times 4^2 + 12 \times 5^2 + 9 \times 6^2}{36} - \left(\frac{14}{3}\right)^2\)

\(= \frac{4 + 36 + 160 + 300 + 324}{36} - \left(\frac{14}{3}\right)^2\)

\(= \frac{824}{36} - \frac{196}{9} = \frac{10}{9}\)