plumiProbability density functions: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 4.1 Probability density 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.
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All 12 questions on Probability density 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, 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, 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, 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, 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
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