The random variable X takes the values 1, 2, 3, 4 only. The probability that X takes the value x is kx(5-x), where k is a constant.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.

1. [1] B1 Table with x values and one correct probability expressed in terms of k. Condone any additional x values if probability stated as 0.
2. [1] B1 Remaining 3 probabilities correct expressed in terms of k – condone if the first correct probability is not in table.
3. [1] B1 Correct value for k SOI. May be calculated in 4(a). SC B1 If denominator 20k used throughout.
4. [1] M1 Accept unsimplified expression. Condone 4k + 12k+18k + 16k. May be implied by use in Variance expression. Special ruling: Allow use of denominator 20k.
5. [1] M1 Appropriate variance formula with their numerical probabilities using their (E(X))², accept unsimplified, with their k substituted. Special ruling: If denominator 20k used throughout, accept appropriate variance formula in terms of k.
6. [1] A1 AG, NFWW.