Complete the probability distribution table for $X$.

Find the expected value of $X$.

     A1A1

Note:     Award A1 for each correct row.

[2 marks]

${\text{E}}(X) = 1 \times \frac{1}{6} + 2 \times \frac{1}{3} + 4 \times \frac{1}{3} + 6 \times \frac{1}{6}$    (M1)

$= \frac{{19}}{6}{\text{ }}\left( { = 3\frac{1}{6}} \right)$    A1

Note:     If the probabilities in (a) are not values between 0 and 1 or lead to ${\text{E}}(X) > 6$ award M1A0 to correct method using the incorrect probabilities; otherwise allow FT marks.

[2 marks]