plumiContinuous random variables: AQA A‑Level Further Maths questions
Every AQA A-Level Further Maths exam question on SD 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, Paper 3 Statistics, Q1 (1 mark): The continuous random variable X has standard deviation 16 Find Var(5X – 12) Circle your answer. [1 mark] 80 400 6388 6400
- June 2025, Paper 3 Statistics, Q4 (6 marks): The continuous random variable X has cumulative distribution function F(x) = { 0 x < 0 sin 3x 0 ≤ x ≤ π 6 1 x > π 6 4 (a) Find P(0.1 < X < 0.3) Give your answer
- June 2025, Paper 3 Statistics, Q5 (6 marks): The discrete random variable D has a discrete uniform distribution taking values 1, 2, 3, …, n The continuous random variable R has a rectangular distribution t
- June 2025, AS Paper 2 Statistics, Q1 (1 mark): The continuous random variable A has probability density function f (a) and variance 16 It is given that f (a) = 0 for a < 0 and ∫ ∞ 0 a2f (a)da = 52 Find the m
- June 2025, AS Paper 2 Statistics, Q4 (5 marks): The discrete random variable X has probability distribution x 1 2 a P(X = x) 0.2 0.7 0.1 where a is a constant greater than 2 4 (a) Find P(X ≥ 2) [1 mark] 4 (b)
- June 2025, AS Paper 2 Statistics, Q6 (6 marks): The continuous random variable A represents the score achieved by a player in a particular game. The probability density function of A is f (a) The probability
- June 2024, Paper 3 Statistics, Q3 (1 mark): The continuous random variable Y has cumulative distribution function F(y) = 0 y < 2 – 1 9 y2 + 10 9 y – 16 9 2 ≤ y < 5 1 y ≥ 5 { Find the median of Y Circle yo
- June 2024, Paper 3 Statistics, Q5 (5 marks): The continuous random variable X has probability density function f(x) = 1 6 e x 3 0 ≤ x ≤ In 27 0 otherwise { Show that the mean of X is 3 2 (In 27 – 2) [5 mar
- June 2024, AS Paper 2 Statistics, Q6 (11 marks): The continuous random variable X has probability density function f(x) = 3x 44 + 1 22 1 ≤ x ≤ 5 0 otherwise { 6 (a) Find P(X > 2) [2 marks] 6 (b) Find the upper
- June 2023, Paper 3 Statistics, Q6 (7 marks): A game consists of two rounds. The first round of the game uses a random number generator to output the score X, a real number between 0 and 10 6 (a) Find P(X >
- June 2023, Paper 3 Statistics, Q8 (14 marks): The continuous random variable X has probability density function f (x) = k sin 2x 0 − x − p 6 0 otherwise 8 < : where k is a constant. 8 (a) Show that k = 4 [4
- June 2023, AS Paper 2 Statistics, Q1 (1 mark): The continuous random variable X has variance 9 The discrete random variable Y has standard deviation 2 and is independent of X Find Var(X + Y ) Circle your ans
- June 2023, AS Paper 2 Statistics, Q8 (8 marks): The continuous random variable X has probability density function f (x) It is given that f (x) = x2 for 0 ≤ x ≤ 1 It is also given that f (x) is a linear functi
- June 2022, Paper 3 Statistics, Q2 (1 mark): The random variable X has probability density function f (x) = 1 0 < x − 1 2 3 8 x×2 1 2 < x − 3 2 0 otherwise 8 > > > > < > > > > : Find P(X < 1) Circle your a
- June 2022, Paper 3 Statistics, Q6 (8 marks): The discrete random variable X has probability distribution function P(X = x) = a x = 0 b x = 1 c x = 2 0 otherwise 8 > > > > > < > > > > > : where a, b and c a
- June 2022, Paper 3 Statistics, Q8 (11 marks): The continuous random variable X has cumulative distribution function F(x) where F(x) = 0 x = 0 ekx × 1 0 − x − 5 1 x > 5 8 > > < > > : 8 (a) Show that k = 1 5
- June 2022, Paper 3 Statistics, Q9 (4 marks): Lianne models the maximum time in hours that a rechargeable battery can be used, before needing to be recharged, with a rectangular distribution with values bet
- June 2022, AS Paper 2 Statistics, Q2 (1 mark): The continuous random variable Y has probability density function f (y) where (1 −1 yf (y) dy = 16 and (1 −1 y2f (y) dy = 1040 Find the standard deviation of Y
- June 2022, AS Paper 2 Statistics, Q5 (11 marks): The continuous random variable X has probability density function f (x) = x3 0 < x × 1 9 1696x3(x2 + 1) 1 < x × 3 0 otherwise 8 > > > < > > > : 5 (a) Find P(X <
- November 2021, Paper 3 Statistics, Q5 (6 marks): The continuous random variable X has cumulative distribution function F(x) = 0 x × 1 1 10x × 1 10 1 < x × 6 1 90x2 + 1 10 6 < x × 9 1 x > 9 8 > > > > > > > < >
- November 2021, AS Paper 2 Statistics, Q6 (11 marks): The continuous random variable X has probability density function f (x) = 1 114 (4x + 7) 0 × x × 6 0 otherwise 8 < : 6 (a) Show that the median of X is 3.87, co
- November 2020, Paper 3 Statistics, Q1 (1 mark): The continuous random variable X has probability density function f (x) = 1 5 1 − x − 6 0 otherwise 8 > < > : Find P(X × 3) Circle your answer. [1 mark] 1 5 2 5
- November 2020, Paper 3 Statistics, Q9 (6 marks): The continuous random variable X has the cumulative distribution function shown below. F(x) = 0 x < 0 1 62 (4x3 + 6x2 + 3x) 0 − x − 2 1 x > 2 8 > > > > < > > >
- November 2020, AS Paper 2 Statistics, Q5 (7 marks): The discrete random variable X has the following probability distribution. x 2 4 6 9 P(X =x) 0.2 0.6 0.1 0.1 5 (a) Find P(X × 6) [1 mark] 5 (b) Let Y = 3X + 2 S
- November 2020, AS Paper 2 Statistics, Q6 (8 marks): The continuous random variable X has probability density function f (x) = 4 45 (x3 × 10x2 + 29x × 20) 1 × x × 4 0 otherwise 8 < : 6 (a) Find P(X < 2) [2 marks]
- June 2019, Paper 3 Statistics, Q4 (7 marks): A random variable X has a rectangular distribution. The mean of X is 3 and the variance of X is 3 4 (a) Determine the probability density function of X. Fully j
- June 2019, Paper 3 Statistics, Q5 (7 marks): An insurance company models the claims it pays out in pounds (£) with a random variable X which has probability density function f (x) = k x 1 < x < a 0 otherwi
- June 2019, AS Paper 2 Statistics, Q4 (8 marks): The continuous random variable X has probability density function f (x) = 4 99(12x − x2 − x3) 0 × x × 3 0 otherwise 8 < : 4 (a) Find P(X > 1) [3 marks] 4 (b) Sh
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