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.