Cumulative distribution functions: Edexcel A‑Level Further Maths questions

Edexcel A-Level Further Maths past-paper questions on 4.2 Cumulative distribution functions, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 14 questions on Cumulative distribution functions, 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, 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 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, 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 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 –
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, 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 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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