20N.1.AHL.TZ0.H_1

pestleMathematicsAAHLPaper 120N· sl-4-7-discrete-random-variablessource ↗

A discrete random variable $X$ has the probability distribution given by the following table.

Given that $E (X) = \frac{19}{12}$ , determine the value of $p$ and the value of $q$ .

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$E (X) = (0 \times p) + (1 \times \frac{1}{4}) + (2 \times \frac{1}{6}) + 3 q (= \frac{19}{12})$ (M1)

$(\Rightarrow \frac{1}{4} + \frac{1}{3} + 3 q = \frac{19}{12})$

$q = \frac{1}{3}$ A1

$p + \frac{1}{4} + \frac{1}{6} + q = 1$ (M1)

$(\Rightarrow p + q = \frac{7}{12})$

$p = \frac{1}{4}$ A1

[4 marks]

Examiners’ report

[N/A]