Cambridge International AS & A Level
* 3 8 1 1 5 3 5 2 0 0 *
FURTHER MATHEMATICS 9231/43
Paper 4 Further Probability & Statistics May/June 2023
1 hour 30 minutes
You must answer on the question paper.
You will need: List of formulae (MF19)
INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● If additional space is needed, you should use the lined page at the end of this booklet; the question
number or numbers must be clearly shown.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
● The total mark for this paper is 50.
● The number of marks for each question or part question is shown in brackets [ ].
This document has 16 pages. Any blank pages are indicated.
DC (CJ) 316286/4
© UCLES 2023 [Turn over
, 2
1 The continuous random variable X has probability density function f given by
` 3
1 -1
- x- 3j
f (x) = *
2
6 x 1 G x G 27,
0 otherwise .
(a) Find the cumulative distribution function of X. [3]
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The random variable Y is defined by Y = X 3 .
(b) Find the probability density function of Y. [3]
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© UCLES 2023 9231/43/M/J/23
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(c) Find the exact value of the median of Y. [2]
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© UCLES 2023 9231/43/M/J/23 [Turn over
* 3 8 1 1 5 3 5 2 0 0 *
FURTHER MATHEMATICS 9231/43
Paper 4 Further Probability & Statistics May/June 2023
1 hour 30 minutes
You must answer on the question paper.
You will need: List of formulae (MF19)
INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● If additional space is needed, you should use the lined page at the end of this booklet; the question
number or numbers must be clearly shown.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
● The total mark for this paper is 50.
● The number of marks for each question or part question is shown in brackets [ ].
This document has 16 pages. Any blank pages are indicated.
DC (CJ) 316286/4
© UCLES 2023 [Turn over
, 2
1 The continuous random variable X has probability density function f given by
` 3
1 -1
- x- 3j
f (x) = *
2
6 x 1 G x G 27,
0 otherwise .
(a) Find the cumulative distribution function of X. [3]
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
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............................................................................................................................................................
1
The random variable Y is defined by Y = X 3 .
(b) Find the probability density function of Y. [3]
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© UCLES 2023 9231/43/M/J/23
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(c) Find the exact value of the median of Y. [2]
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© UCLES 2023 9231/43/M/J/23 [Turn over
