The random variable X takes the values −1, 1, 2, 3 only. The probability that X takes the value x is kx², where k is a constant.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.

1. [B1] Probability distribution table with correct values of x, no additional values unless with probability 0 stated, at least one correct probability including k
2. [M1] Equating Σp = 1, may be implied by answer
3. [A1] If 0 scored, SCB2 for probability distribution table with correct numerical probabilities.
4. [B1FT] FT if 0< their k<1
5. [M1] Correct formula for variance, in terms of k at least – must have ‘– mean²’(ft).
6. [A1]
7. [B1FT] FT if 0< their k<1
8. [M1] Subst their values in correct var formula – must have ‘– mean²’(ft) (condone probs not summing to exactly 1)
9. [A1] Using their values from (i)