The probability distribution table for a random variable X is shown below. x -2 -1 0.5 1 2 P(X = x) 0.12 p q 0.16 0.3 Given that E(X) = 0.28, find the value of p and the value of q.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [B1] Sum of probabilities = 1 p + q = 0.42 OE.
2. [B1] Form equation using E(X) = 0.28 -p + 0.5q = -0.24 OE. Accept unsimplified.
3. [M1] Either Substitution method to form a single equation in either p or q and finding values for both unknowns. Or Elimination method by writing both equations in the same form (usually ap + bq = c) and + or to find an equation in one unknown and finding values for both unknowns.
4. [A1] CAO, both WWW. If M0 awarded SC B1 for both correct WWW.