plumiContinuous distributions: Edexcel A‑Level Further Maths questions
Every Edexcel 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 Further Statistics 2, question 5: The random variable X ~ U[1, 4] (a) Find (i) P (1.8 < X < 3.2) (ii) P (X > 3.2 | X > 1.8) (3) A random sample of 10 observations of X is taken. The random varia](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/9fm0-4b-jun25-05-qp.webp)
![June 2024 Further Statistics 2, question 4: The random variable G has a continuous uniform distribution over the interval [– 3, 15] (a) Calculate P(G > 12) (1) The random variable H has a continuous unifo](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/9fm0-4b-jun24-04-qp.webp)
![June 2024 AS Further Statistics 2, question 4: The continuous random variable X is uniformly distributed over the interval [2, 7] (a) Write down the value of E(X) (1) (b) Find P(1 < X < 4) (1) (c) Find P(2X](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/8fm0-24-jun24-04-qp.webp)
![June 2023 Further Statistics 2, question 7: The random variable R has a continuous uniform distribution over the interval [2, 10] (a) Write down the probability density function f(r) of R (1) A sphere of](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/9fm0-4b-jun23-07-qp.webp)
![June 2023 AS Further Statistics 2, question 4: The random variable X has a continuous uniform distribution over the interval [−3, k] Given that P 4 2 1 3 X (a) find the value of k (3) A computer generates](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/8fm0-24-jun23-04-qp.webp)
![June 2022 Further Statistics 2, question 7: A rectangle is to have an area of 40 cm2 The length of the rectangle, L cm, follows a continuous uniform distribution over the interval [4, 10] Find the expecte](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/9fm0-4b-jun22-07-qp.webp)
![June 2022 AS Further Statistics 2, question 5: The random variable X has the continuous uniform distribution over the interval [0.5, 2.5] Talia selects a number, T, at random from the distribution of X (a) F](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/8fm0-24-jun22-05-qp.webp)
![November 2020 Further Statistics 2, question 8: 8 A circle, centre O, has radius x cm, where x is an observation from the random variable X which has a rectangular distribution on [0, π] (a) Find the probabil](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/9fm0-4b-nov20-08-qp.webp)
All 26 questions on Continuous distributions, as a list
- June 2025, Further Statistics 2, Q5 (11 marks): The random variable X ~ U[1, 4] (a) Find (i) P (1.8 < X < 3.2) (ii) P (X > 3.2 | X > 1.8) (3) A random sample of 10 observations of X is taken. The random varia
- June 2025, AS Further Statistics 2, Q2 (9 marks): The graph of the probability density function f(x) of the continuous uniform random variable X is shown below. –4 –3 –2 –1 0.1 0.3 0 1 2 3 4 x f(x) (a) Write do
- June 2025, AS Further Statistics 2, Q4 (11 marks): Subrat is modelling the time, t seconds, it takes for a computer to carry out a particular process. He models the time using the continuous random variable T wi
- June 2024, Further Statistics 2, Q4 (9 marks): The random variable G has a continuous uniform distribution over the interval [– 3, 15] (a) Calculate P(G > 12) (1) The random variable H has a continuous unifo
- June 2024, Further Statistics 2, Q5 (10 marks): A continuous random variable X has probability density function f otherwise ( ) x ax bx x 2 3 0 2 < where a and b are constants. Given that P(X 4) = 3 8
- June 2024, AS Further Statistics 2, Q1 (8 marks): A continuous random variable X has cumulative distribution function F(x) given by F( ) ( ) ( ) x x x x x x x 0 1 1 5 1 1 0 1 1 20 4 0 4 1 4 2
- June 2024, AS Further Statistics 2, Q3 (9 marks): The continuous random variable Y has probability density function f otherwise ( ) ( )( ) y y y y 1 24 2 4 0 3 0 (a) Show that the mode of Y is 1, just
- June 2024, AS Further Statistics 2, Q4 (8 marks): The continuous random variable X is uniformly distributed over the interval [2, 7] (a) Write down the value of E(X) (1) (b) Find P(1 < X < 4) (1) (c) Find P(2X
- June 2023, Further Statistics 2, Q6 (10 marks): The continuous random variable X has cumulative distribution function given by F ( ) x x k x ax x x 0 0 0 4 1 4 2 < > The values of a and k are positive constan
- June 2023, Further Statistics 2, Q7 (9 marks): The random variable R has a continuous uniform distribution over the interval [2, 10] (a) Write down the probability density function f(r) of R (1) A sphere of
- June 2023, AS Further Statistics 2, Q2 (11 marks): A continuous random variable X has probability density function f 1 3 otherwise ( ) ( ) x x x x 16 9 0 2 (a) Find the cumulative distribution function of X
- June 2023, AS Further Statistics 2, Q4 (9 marks): The random variable X has a continuous uniform distribution over the interval [−3, k] Given that P 4 2 1 3 X (a) find the value of k (3) A computer generates
- June 2022, Further Statistics 2, Q7 (7 marks): A rectangle is to have an area of 40 cm2 The length of the rectangle, L cm, follows a continuous uniform distribution over the interval [4, 10] Find the expecte
- June 2022, Further Statistics 2, Q8 (12 marks): The continuous random variable X has cumulative distribution function given by F( ) . . . x x x x x x = − − 1 5 0 0 25 1 1 25 1 1 3 3 2 < > (a) Find
- June 2022, AS Further Statistics 2, Q2 (5 marks): The graph shows the probability density function f(x) of the continuous random variable X 12 11 10 9 8 7 6 5 4 3 2 1 O x f(x) 0.20 0.15 0.10 0.05 (a) Find P(X <
- June 2022, AS Further Statistics 2, Q4 (9 marks): A random variable X has probability density function given by f otherwise ( ) . . x x x = − − 0 8 6 4 0 2 4 3 The median of X is m (a) Show that m3 –
- June 2022, AS Further Statistics 2, Q5 (9 marks): The random variable X has the continuous uniform distribution over the interval [0.5, 2.5] Talia selects a number, T, at random from the distribution of X (a) F
- November 2021, Further Statistics 2, Q3 (10 marks): The continuous random variable X has cumulative distribution function given by F( ) . . x x x x x = − 0 2 1 25 2 5 2 10 1 10 < > (a) Find P ({X
- November 2020, Further Statistics 2, Q5 (10 marks): 5 y x O 2π Figure 1 The random variable X has probability density function f (x) and Figure 1 shows a sketch of f (x) where f (x) = (1 cos ) 0 2 0 otherwise k x
- November 2020, Further Statistics 2, Q8 (11 marks): 8 A circle, centre O, has radius x cm, where x is an observation from the random variable X which has a rectangular distribution on [0, π] (a) Find the probabil
- November 2020, AS Further Statistics 2, Q3 (14 marks): The continuous random variable X has cumulative distribution function F( ) x px k x x x x = − 0 1 4 4 9 9 < > where p and k are constants. (a) Fin
- June 2019, Further Statistics 2, Q4 (8 marks): 4 The continuous random variable ;has cumulative distribution function given by F( ) x k x x x x x = − ⎛ ⎝⎜ ⎞ ⎠⎟ ⎧ ⎨ ⎪⎪ ⎩ ⎪ ⎪ 0 3 8 1 0 0 2 2 3 4 - - < > where
- June 2019, AS Further Statistics 2, Q2 (9 marks): Lloyd regularly takes a break from work to go to the local cafe. The amount of time Lloyd waits to be served, in minutes, is modelled by the continuous random v
- June 2019, AS Further Statistics 2, Q4 (10 marks): The random variable X has a continuous uniform distribution over the interval [5, a], where a is a constant. Given that Var(X ) = 27 4 (a) show that a = 14 (3)
- June 2018, AS Further Statistics 2, Q2 (8 marks): The continuous random variable X has probability density function f otherwise ( ) x x = 1 8 1 9 0 (a) Write down the name given to this distribution
- June 2018, AS Further Statistics 2, Q4 (9 marks): The continuous random variable X has cumulative distribution function F( ) . x c x x x x n = − 0 4 5 1 3 3 9 9 < > where c is a positive constant an
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