Further Mathematics · Pearson Edexcel 9FM0 · Option FS1 · Topic 1

Discrete probability distributions

Random variables that take separate values. You find their mean (expected value) and variance, including for functions of the variable.

1 sub-topic
Taught in Year 12
19 practice questions
1 animated lesson

Practice questions (19) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

1.1Discrete probability distributionsY12

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Easy and medium questions from this topic, each with a worked solutions and the mark for every step. All 19 questions in this topic, free, no account needed.

Discrete probability distributions

Easy

E(X²) for a discrete distribution · Year 12 · 1 mark

A discrete random variable has $\mathrm{P}(X = 2) = 0.1$ , $\mathrm{P}(X = 3) = 0.6$ , $\mathrm{P}(X = 4) = 0.3$ . What is $\mathrm{E}(X^2)$ ?
(1)

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$\mathrm{E}(X^2)$ ${}= \sum x^2\,\mathrm{P}(X = x)$ . It is not the square of $\mathrm{E}(X)$ . $C$ : 10.6

Total1

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Discrete probability distributions

Medium

A discrete random variable · Year 12 · 7 marks

The discrete random variable

X

has the probability distribution:

\mathrm{P}(X = 1)

{}= p, \ \mathrm{P}(X = 2)

{}= q, \ \mathrm{P}(X = 3)

{}= 0.4, \ \mathrm{P}(X = 4)

{}= 0.1

. Given that

\mathrm{E}(X) = 2.4

,

(a)
find the values of $p$ and $q$ .
(3)
(b)
Find $\operatorname{Var}(X)$ .
(3)
(c)
Find $\operatorname{Var}(1 + 3X)$ .
(1)

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Part (a)3 marks

The probabilities add to 1. $p + q = 0.5$
Use $\mathrm{E}(X)$ ${}= \sum x \mathrm{P}(X = x)$ . $p + 2q + 1.6 = 2.4$
$p = 0.2, \ q = 0.3$

Part (b)3 marks

$\sum x^{2} \mathrm{P}(X = x)$ . $\mathrm{E}(X^2) = 6.6$
$\operatorname{Var}(X)$ ${}= 6.6 - 2.4^2$ ${}= 0.84$

Part (c)1 mark

$\operatorname{Var}(aX + b)$ ${}= a^{2} \operatorname{Var}(X)$ . $9 \times 0.84 = 7.56$

Total7

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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