plumiContinuous random variables: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on S2.2 Continuous random variables, 2019–2025, with its mark scheme and examiner’s report.
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All 28 questions on Continuous random variables, as a list
- June 2025, Statistics 2 (S2), Q1 (11 marks): The continuous random variable X has cumulative distribution function given by F ( ) x x k x x x 0 0 6 0 1 1 2 4 < x > 1 where k is a positive con
- June 2025, Statistics 2 (S2), Q5 (11 marks): In this question solutions relying entirely on calculator technology are not acceptable. The continuous random variable X has a probability density function giv
- January 2025, Statistics 2 (S2), Q4 (10 marks): (i) The probability density function of a continuous random variable X is given by f otherwise ( ) x x x 3 20 1 3 0 (a) Using algebraic integration find E
- January 2025, Statistics 2 (S2), Q7 (10 marks): A continuous random variable X has probability density function defined as f otherwise ( ) ( ) x k x x 3 2 6 0 2 (a) Sketch the graph of y = f (x) (b) Hen
- October 2024, Statistics 2 (S2), Q5 (9 marks): The continuous random variable X has a probability density function given by 1 3 1 4 1 2 f ( ) 4 1 2 3 4 2 4 0 otherwis 3 e x x x x x x
- October 2024, Statistics 2 (S2), Q7 (15 marks): The continuous random variable X has probability density function given by 0 f ( ) 4 8 0 otherw 4 ise ax x x b c x x < where a, b and c are constants. f(x)
- June 2024, Statistics 2 (S2), Q2 (9 marks): 2 The continuous random variable H has cumulative distribution function given by F ( ) h h h h h h h h h d h d 0 0 48 0 4 6 1 3 4 5 3 10 75 2 3 5 1 2 2
- June 2024, Statistics 2 (S2), Q6 (16 marks): 6 In this question solutions relying entirely on calculator technology are not acceptable. The continuous random variable X has the following probability densit
- January 2024, Statistics 2 (S2), Q4 (12 marks): The continuous random variable G has probability density function f(g) given by f(g) = otherwise g g g 1 15 3 1 2 3 20 2 4 0 ( ) < < (a)
- January 2024, Statistics 2 (S2), Q7 (8 marks): A continuous random variable X has cumulative distribution function F(x) given by F(x) = x k ax bx x x x 0 1 4 1 2 1 2 3 4 < > ( ) where a, b an
- October 2023, Statistics 2 (S2), Q2 (8 marks): The continuous random variable X has probability density function f(x) given by f otherwise ( ) x ax x bx c x d 3 0 4 0 4 < where a, b, c and d are c
- October 2023, Statistics 2 (S2), Q6 (12 marks): The continuous random variable Y has cumulative distribution function given by F( ) y y y y y y k k y y 0 0 1 21 2 15 6 2 7 5 1 0 6
- June 2023, Statistics 2 (S2), Q3 (9 marks): The continuous random variable X has probability density function given by f otherwise ( ) x x x c x 1 48 8 0 2 5 2 (a) Show that c = 31 (b) Find
- June 2023, Statistics 2 (S2), Q5 (14 marks): A continuous random variable Y has cumulative distribution function given by F( ) y y y a y b y y c y 0 1 16 6 1 12 1 12 100 5 1
- January 2023, Statistics 2 (S2), Q6 (18 marks): The continuous random variable X has cumulative distribution function F x ax bx 0 1 2 x < 0 0 x k x > k where a, b and k are positive constants. (a)
- October 2022, Statistics 2 (S2), Q2 (15 marks): A random variable X has probability density function given by f(x) = 1 4 1 2 1 2 2 3 4 1 2 0 − − x x x k < otherwise where k is a positiv
- October 2022, Statistics 2 (S2), Q5 (9 marks): The continuous random variable X has cumulative distribution function given by F(x) = 0 3 1 6 3 3 4 3 7 6 4 1 1 6 7 1 7 2 2 x x x x x c d x c x x < < < < ( ) (
- June 2022, Statistics 2 (S2), Q2 (11 marks): The time, in minutes, spent waiting for a call to a call centre to be answered is modelled by the random variable T with probability density function f otherwis
- June 2022, Statistics 2 (S2), Q6 (13 marks): The continuous random variable X has probability density function f 2 4 otherwise ( ) . ( ) x x kx x a x x x = − 0 1 8 0 0 2 4 6 < < < where
- January 2022, Statistics 2 (S2), Q4 (15 marks): 4 The continuous random variable X has a probability density function given by f otherwise ( ) ( ) ( ) x k x x k x k x x = − − 1 2 1 1 3 3 6 1
- October 2021, Statistics 2 (S2), Q3 (10 marks): A continuous random variable X has cumulative distribution function F( ) x ax a bx x x x x x = − + ( ) 0 4 1 1 0 0 1 1 3 3 2 3 4 < < > where
- October 2021, Statistics 2 (S2), Q6 (17 marks): The continuous random variable Y has probability density function f(y) given by f otherwise ( ) y y y y y y = + ( ) − − ( ) 1 14 2 1 1 3 14 1 3
- June 2021, Statistics 2 (S2), Q3 (15 marks): The continuous random variable Y has the following probability density function f(y) = 6 25 1 1 2 3 50 4 2 4 0 2 3 ( ) ( ) y y y y y − − <
- June 2021, Statistics 2 (S2), Q5 (11 marks): A game uses two turntables, one red and one yellow. Each turntable has a point marked on the circumference that is lined up with an arrow at the start of the ga
- January 2021, Statistics 2 (S2), Q2 (10 marks): The distance, in metres, a novice tightrope artist, walking on a wire, walks before falling is modelled by the random variable W with cumulative distribution fu
- January 2021, Statistics 2 (S2), Q4 (10 marks): A continuous random variable X has probability density function f otherwise ( ) ( ) x k a x x a = − 2 0 0 where k and a are constants. (a) Show that k
- October 2020, Statistics 2 (S2), Q1 (8 marks): f(x) O 1 2 3 x Figure 1 Figure 1 shows a sketch of the probability density function f(x) of the random variable X. For 1 x 2, f(x) is represented by a curve
- October 2020, Statistics 2 (S2), Q5 (13 marks): The waiting time, T minutes, of a customer to be served in a local post office has probability density function f( ) = t t 1 50 18 2 1 20 0 ( ) 0 t 3 3 ˂
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