plumiContinuous distributions: OCR MEI A‑Level Further Maths questions
Every OCR MEI A-Level Further Maths exam question on FS.4 Continuous distributions, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 Statistics Major, question 5: The random variable X has a continuous uniform distribution over [ 4 2 , ] . - (a) Find the variance of X. [2] (b) Determine the probability that if two indepen](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42201-jun25-05-qp.webp?v=3)
![June 2023 Statistics Major, question 8: The random variable X has a continuous uniform distribution over [0, 10]. (a) Find the probability that, if two independent values of X are taken, one is less t](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42201-jun23-08-qp.webp?v=3)
![November 2021 Statistics Major, question 11: The continuous random variable X has probability density function given by Z ] 2 ax 0 x 2 , 1 G ] 2 f ( ) x b ( 3 x ) 2 x 3 , [ = - G G ]] 0 otherwise , \ where](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42201-nov21-11-qp.webp?v=3)
![June 2018 AS Statistics B, question 4: The random variable X has a continuous uniform distribution on [0, 10]. ^ h. (i) Find P X [1] 3 1 1 6 (ii) Find each of the following. • E(X) • Var(X) [2] Maris](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y41601-jun18-04-qp.webp?v=3)
All 20 questions on Continuous distributions, as a list
- June 2025, Statistics Major, Q5 (4 marks): The random variable X has a continuous uniform distribution over [ 4 2 , ] . - (a) Find the variance of X. [2] (b) Determine the probability that if two indepen
- June 2025, Statistics Major, Q11 (16 marks): The function F(x) is defined as follows. x 0 1 0 * ax b 4 F x ( ) + 0 x 5 = - G G 9 x 15 3 + 1 x 2 5 where a and b are constants. You are given that F(1) = 0.5
- June 2024, Statistics Major, Q4 (7 marks): An archer fires arrows at a circular target of radius 50 cm. The distance in cm that an arrow lands from the centre of the target is modelled by the random vari
- June 2024, Statistics Major, Q10 (9 marks): Ben takes an underground train to work and back home each day. The waiting time is defined as the time from when he reaches the station platform until he boards
- June 2024, Statistics Major, Q12 (9 marks): The cumulative distribution function of the continuous random variable X is given by x 0 1 20 , * ^ h 2 F ( ) x a x bx c 20 x 30 , = + + G G 1 x 2 30 , where a,
- June 2023, Statistics Major, Q8 (12 marks): The random variable X has a continuous uniform distribution over [0, 10]. (a) Find the probability that, if two independent values of X are taken, one is less t
- June 2023, Statistics Major, Q10 (15 marks): The continuous random variable X has probability density function given by c a m 4 7 * 2 3 x 1 x 2 , + - G G 15 2 f ( ) x 2 x = 0 otherwise, where a is a positi
- June 2022, Statistics Major, Q12 (14 marks): The continuous random variable X has cumulative distribution function given by 0 x 0 , * 1 2 F ( ) x k ax ( 0 5 . x ) 0 x a , = - G G 1 x 2 a , where a and k ar
- June 2022, AS Statistics B, Q2 (6 marks): The continuous random variable X has cumulative distribution function given by 0 x a , 1 * x a - x a x b F ( ) , = G G b a - 1 x 2 b , where a and b are constan
- June 2022, AS Statistics B, Q5 (8 marks): Layla works at an internet café. Each terminal at the café has its own keyboard, and keyboards need to be replaced whenever faults develop. Layla knows that the
- June 2022, AS Statistics B, Q7 (9 marks): Many cars have pollen filters to try to remove as much pollen as possible from the passenger compartment. In a test car, the amount of pollen is regularly monit
- November 2021, Statistics Major, Q10 (9 marks): Sarah takes a bus to work each weekday morning and returns each evening. The times in minutes that she has to wait for the bus in the morning and evening are mo
- November 2021, Statistics Major, Q11 (11 marks): The continuous random variable X has probability density function given by Z ] 2 ax 0 x 2 , 1 G ] 2 f ( ) x b ( 3 x ) 2 x 3 , [ = - G G ]] 0 otherwise , \ where
- November 2021, AS Statistics B, Q6 (11 marks): The probability density function of the continuous random variable X is given by ' 2 1 ( ax ) 0 x 1 , + G G x f ( ) = 0 otherwise, where a is a constant. (a) Sh
- November 2020, Statistics Major, Q11 (18 marks): The length of time in minutes for which a particular geyser erupts is modelled by the continuous random variable T with cumulative distribution function given b
- June 2019, Statistics Major, Q9 (15 marks): Every weekday Jonathan takes an underground train to work. On any weekday the time in minutes that he has to wait at the station for a train is modelled by the
- June 2019, Statistics Major, Q10 (14 marks): The probability density function of the continuous random variable X is given by m = * kx 0 x a , G G f ( ) x 0 otherwise, where a, k and m are positive constan
- June 2019, AS Statistics B, Q4 (12 marks): The cumulative distribution function of the continuous random variable X is given by 0 x 1 0 , * 2 F ( ) x k ( 12 x x ) 0 x 2 , = - G G 1 x 2 , 2 where k is a c
- June 2018, AS Statistics B, Q3 (10 marks): The probability density function of the continuous random variable X is given by c x c x 0 , + - G G * ^ h x c x x c f 0 , = - G G 0 otherwise, where c is a pos
- June 2018, AS Statistics B, Q4 (15 marks): The random variable X has a continuous uniform distribution on [0, 10]. ^ h. (i) Find P X [1] 3 1 1 6 (ii) Find each of the following. • E(X) • Var(X) [2] Maris
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