CAIE A-Level Mathematics A2 5.4.1 Discrete Random Variables Questions

Practise constructing probability distributions and calculating expectations for discrete random variables.

Exam points

construct probability distribution tables for discrete random variables
use distribution probabilities to find unknown constants
calculate and interpret expected values from a distribution

[Maximum number: 6]

The numbers on the faces of a fair six-sided dice are 1,2,2,3,3,3. The random variable X is the total score when the dice is rolled twice.

(a)

Draw up the probability distribution table for X.

[ 3 ]

The probability distribution is

x	2	3	4	5	6
P(X=x)	$\frac{1}{36}$	$\frac{4}{36}=\frac19$	$\frac{10}{36}=\frac5{18}$	$\frac{12}{36}=\frac13$	$\frac{9}{36}=\frac14$

(b)

Find the value of $\operatorname{Var}(X)$ .

[ 3 ]

The mean is
$E(X)=\frac{1(2)+4(3)+10(4)+12(5)+9(6)}{36}=\frac{14}{3}.$
Therefore,
$\begin{aligned} \operatorname{Var}(X) &=\frac{1(2^2)+4(3^2)+10(4^2)+12(5^2)+9(6^2)}{36}-\left(\frac{14}{3}\right)^2\\ &=\frac{10}{9}. \end{aligned}$

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CAIE A-Level Mathematics A2 5.4.1 Discrete Random Variables Questions question 1

Question (a)

Question (b)