plumiProbability density functions: OCR MEI A‑Level Further Maths questions
OCR MEI 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 13 questions on Probability density functions, as a list
- 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 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, 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, 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
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