Find the value of k .

Find \({\text{E}}(X)\) .

evidence of summing to 1     (M1)

e.g. \(\sum\limits_{}^{} {p = 1{\text{, }}0.3 + k + 2k + 0.1 = 1} \)

correct working     (A1)

e.g. \(0.4 + 3k{\text{, }}3k = 0.6\)

\(k = 0.2\)    A1     N2

[3 marks]

correct substitution into formula \({\text{E}}(X)\)      (A1)

e.g. \(0(0.3) + 2(k) + 5(2k) + 9(0.1){\text{, }}12k + 0.9\)

correct working 

e.g. \(0(0.3) + 2(0.2) + 5(0.4) + 9(0.1){\text{, }}0.4 + 2.0 + 0.9\)     (A1)

\({\text{E}}(X)\)= 3.3     A1     N2

[3 marks]

Overall, this question was very well done. A few candidates left this question blank, or used methods which would indicate they were unfamiliar with discrete random variables. In part (b), there were a good number of candidates who set up their work correctly, but then had trouble adding or multiplying decimals without a calculator. A common type of error for these candidates was \(5(0.4) = 0.2\) .

Overall, this question was very well done. A few candidates left this question blank, or used methods which would indicate they were unfamiliar with discrete random variables. In part (b), there were a good number of candidates who set up their work correctly, but then had trouble adding or multiplying decimals without a calculator. A common type of error for these candidates was \(5(0.4) = 0.2\) .