plumiContinuous random variables: WJEC A‑Level Further Maths questions
Every WJEC A-Level Further Maths exam question on 2.2 Continuous random variables, 2018–2025, with its mark scheme and examiner’s report.
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All 10 questions on Continuous random variables, as a list
- Summer 2025, Unit 5, Q2 (5 marks): The continuous random variable X is uniformly distributed over the interval (–θ, θ ), where θ is 2. an unknown constant. Find X 2 E (a) . [4] Hence, write d
- Summer 2025, AS Unit 2, Q6 (15 marks): 6. (a) The random variable X has a probability density function given by { ke–kx x x 0 f x ( ) = 0 otherwise (i) What is the name of the distribution that X fol
- Summer 2024, Unit 5, Q5 (19 marks): The probability density function of the continuous random variable X is given by 5. 3 2 x f x ( ) for 0 X x X 3 f x ( ) 0 otherwise. X is the mean of a
- Summer 2024, AS Unit 2, Q2 (13 marks): 2. Emlyn aims to produce podcast episodes that are a standard length of time, which he calls the ‘target time’. The time, X minutes, above or below the target t
- Summer 2023, AS Unit 2, Q4 (12 marks): 4. A continuous random variable X has cumulative distribution function F given by ⎧ 0 for x < 0, ⎪ 1 ⎪⎪ 4 x for 0 X x X 2, F(x) = ⎨ 480 x4 + 7 1 ⎪ for 2 < x X b
- Summer 2022, AS Unit 2, Q4 (12 marks): The continuous random variable R has probability density function f(r) given by 4. ( ) f r( ) = kr b − r ⎧ 1 X r X 4, for ⎨ 0 otherwise, ⎩ where k and b are pos
- Summer 2019, Unit 5, Q2 (6 marks): 2. The continuous random variable X is uniformly distributed over the interval (θ – 1, θ + 5), where θ is an unknown constant. (a) Find the mean and the varianc
- Summer 2019, Unit 5, Q8 (18 marks): 8. The random variable X has probability density function ( ) = 1 + 3λx − 1 2 X x X 1 , f x for 2 2 ( ) = 0 otherwise, f x where λ is an unknown parameter such
- Summer 2019, AS Unit 2, Q4 (15 marks): 4. The continuous random variable, X, has the following probability density function kx for 0 X x~1, ⎧ ⎨⎪ kx3 for 1X xX 2, f (x) = ⎩⎪ 0 otherwise, where k is a
- Summer 2018, AS Unit 2, Q2 (15 marks): 2. The length of time a battery works, in tens of hours, is modelled by a random variable X with cumulative distribution function for x ! 0, 0 ⎧ x3 ⎪ F x( ) = (
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