The random variable X takes the values -2, -1, 0, 2, 3. It is given that P(X = x) = k(x² + 2), where k is a positive constant.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

1. [B1] k must be identified
2. [M1] Table with correct outcomes and 2 correct probabilities. FT substituting their k correctly into formula, with 0 < p < 1. No additional x values unless probability 0. Condone in terms of k of the form 6k/28 or 6k.
3. [A1] Fully correct. Decimal answers to at least 3 sig figures, condone not summing exactly to 1.
4. [M1] Accept unsimplified expression. May be calculated in the variance. FT their table with 5 probabilities 0 <p< 1 that sum to 1.
5. [M1] Appropriate variance formula using their (E(X))² value. FT their table with at least 4 probabilities 0 < p < 1, that may not sum to 1.
6. [A1] Condone 825/196. If one or both M marks not awarded, SC B1 for correct answer WWW.