19N.1.AHL.TZ0.H_1

pestleMathematicsAAHLPaper 119N· sl-4-7-discrete-random-variablessource ↗

The probability distribution of a discrete random variable, $X$ , is given by the following table, where $N$ and $p$ are constants.

Find the value of $p$ .

[2]

Given that ${\text{E}}\left( X \right) = 10$ , find the value of $N$ .

[3]

Markscheme / solution

$p = 1 - \frac{1}{2} - \frac{1}{5} - \frac{1}{5}$ (M1)

$= \frac{1}{{10}}$ A1

[2 marks]

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

$\frac{1}{2} + 1 + 2 + \frac{N}{{10}} = 10$ A1

$\Rightarrow N = 65$ A1

Note: Do not allow FT in part (b) if their $p$ is outside the range $0 < p < 1$ .

[3 marks]

Examiners’ report

[N/A]