A discrete random variable X has a probability distribution given in the following table.

(a)     ${\text{E}}(X) = 2.61$, determine the value of p and of q.

(b)     Calculate ${\text{Var}}(X)$ to three significant figures.

(a)     $p + q = 0.44$     A1

$2.5p + 3.5q = 1.25$     (M1)A1

$p = 0.29,{\text{ }}q = 0.15$     A1

(b)     use of ${\text{Var}}(X) = {\text{E}}({X^2}) - {\text{E}}{(X)^2}$     (M1)

${\text{Var}}(X) = 2.10$     A1

[6 marks]

An easy question, well answered by most candidates. For the others it was disappointing that many did not use the fact that the probabilities add to unity.