19M.1.SL.TZ2.S_1

pestleMathematicsAASLPaper 119M· sl-4-7-discrete-random-variablessource ↗

The following table shows the probability distribution of a discrete random variable $X$ .

Find the value of $k$ .

[3]

Find ${\text{E}}\left( X \right)$ .

[3]

Markscheme / solution

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

evidence of using $\sum {p = 1}$ (M1)

correct working (A1)

eg $\frac{3}{{13}} + \frac{1}{{13}} + \frac{4}{{13}} + k = 1$ , $1 - \frac{8}{{13}}$

$k = \frac{5}{{13}}$ A1 N2

[3 marks]

valid approach to find ${\text{E}}\left( X \right)$ (M1)

eg $1 \times \frac{1}{{13}} + 2 \times \frac{4}{{13}} + 3 \times k$ , $0 \times \frac{3}{{13}} + 1 \times \frac{1}{{13}} + 2 \times \frac{4}{{13}} + 3 \times \frac{5}{{13}}$

correct working (A1)

eg $\frac{1}{{13}} + \frac{8}{{13}} + \frac{{15}}{{13}}$

${\text{E}}\left( X \right) = \frac{{24}}{{13}}$ A1 N2

[3 marks]

Examiners’ report

[N/A]