The random variable X has the following probability distribution.

Given that ${\rm{E}}(X) = 1.7$ , find q .

correct substitution into ${\rm{E}}(X) = \sum {px}$ (seen anywhere)     A1

e.g. $1s + 2 \times 0.3 + 3q = 1.7$ , $s + 3q = 1.1$

recognizing $\sum {p = 1}$ (seen anywhere)     (M1)

correct substitution into $\sum {p = 1}$     A1

e.g. $s + 0.3 + q = 1$

attempt to solve simultaneous equations     (M1)

correct working     (A1)

e.g. $0.3 + 2q = 0.7$ , $2s = 1$

$q = 0.2$     A1     N4

[6 marks]

Candidates generally earned either full marks or only one mark on this question. The most common error was where candidates only wrote the equation for ${\rm{E}}(X) = 1.7$ , and tried to rearrange that equation to solve for q. The candidates who also knew that the sum of the probabilities must be equal to 1 were very successful in solving the resulting system of equations.