plumiDiscrete random variables and expectation: AQA A‑Level Further Maths questions
Every AQA A-Level Further Maths exam question on SA Discrete random variables and expectation, 2019–2025, with its mark scheme and examiner’s report.
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All 33 questions on Discrete random variables and expectation, as a list
- June 2025, Paper 3 Statistics, Q2 (1 mark): The discrete random variable Y has probability distribution y – 6 2 3 18 P(Y = y) 0.56 0.02 0.21 0.21 Find the mode of Y Circle your answer. [1 mark] – 6 0.21 0
- 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, Paper 3 Statistics, Q7 (8 marks): A company sells a particular type of game. In the game, a player can score 0, 10 or 100 points. The probability of scoring 10 points is 0.37 The probability of
- June 2025, AS Paper 2 Statistics, Q3 (1 mark): The random variable T has a discrete uniform distribution and takes values 1, 2, 3, …, 17 Find the standard deviation of T Circle your answer. [1 mark] 8√ 3 3 2
- 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 2024, Paper 3 Statistics, Q7 (4 marks): The random variable X has a discrete uniform distribution and takes values 1, 2, 3, …, n The random variable Y has probability distribution function P(Y = y) =
- June 2024, Paper 3 Statistics, Q8 (5 marks): The discrete random variable X has probability distribution x 7 13 17 21 P(X = x) 0.4 0.35 0.1 0.15 Show that P(X ≤ 17 │ X > E(X )) = 0.75 [5 marks]
- June 2024, AS Paper 2 Statistics, Q1 (1 mark): The discrete random variable X has probability distribution function P(X = x) = 0.45 x = 1 0.25 x = 2 0.25 x = 3 0.05 x = 4 0 otherwise { State the mode of X Ci
- June 2024, AS Paper 2 Statistics, Q4 (7 marks): The discrete random variable Y has probability distribution y 15 21 36 43 P(Y = y) 0.16 0.32 0.29 0.23 The standard deviation of Y is s 4 (a) Show that s = 10.5
- June 2024, AS Paper 2 Statistics, Q5 (6 marks): A spinner has 8 equal areas numbered 1 to 8, as shown in the diagram below. 8 4 2 1 7 3 5 6 The spinner is spun and lands with one of its edges on the ground. 5
- June 2023, Paper 3 Statistics, Q1 (1 mark): The discrete random variable A takes only the values 0, 2 and 4, and has cumulative distribution function F(a) = P(A − a) a 0 2 4 F(a) 0.2 0.6 1 Find P(A = 2) C
- 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, AS Paper 2 Statistics, Q2 (1 mark): The random variable T has a discrete uniform distribution and takes the values 1, 2, 3, 4 and 5 Find the variance of T Circle your answer. [1 mark] 1 5 4 3 2 13
- June 2023, AS Paper 2 Statistics, Q3 (3 marks): The discrete random variable X has probability distribution x – 4 3 8 P(X = x) 0.2 0.7 0.1 Show that E(5X – 7) = 3.5 [3 marks]
- June 2022, Paper 3 Statistics, Q1 (1 mark): The random variable T follows a discrete uniform distribution and can take values 1, 2, 3, …, 16 Find the variance of T Circle your answer. [1 mark] 1.25 18.75
- 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, AS Paper 2 Statistics, Q1 (1 mark): The discrete random variable X has the following probability distribution x −15 18 29 P(X =x) 0.2 0.7 0.1 Find P(X > 18) Circle your answer. [1 mark] 0.1 0.2 0.
- June 2022, AS Paper 2 Statistics, Q3 (7 marks): The discrete random variable A has the following probability distribution function P(A = a) = 0:45 a = 0 0:25 a = 1 0:3 a = 2 0 otherwise 8 > > > < > > > : 3 (a
- 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, Q1 (1 mark): The discrete uniform distribution X can take values 1, 2, 3, …, 10 Find P(X − 7) Circle your answer. [1 mark] 0.3 0.4 0.6 0.7
- November 2021, Paper 3 Statistics, Q2 (1 mark): The random variable X has variance Var (X) Which of the following expressions is equal to Var (aX + b), where a and b are non-zero constants? Circle your answer
- November 2021, Paper 3 Statistics, Q3 (5 marks): In a game, it is only possible to score 10, 20 or 30 points. The probability of scoring 20 points is twice the probability of scoring 30 points. The probability
- November 2021, AS Paper 2 Statistics, Q1 (1 mark): The discrete random variable X has Var(X) = 6:5 Find Var(4X − 2) Circle your answer. [1 mark] 24 26 102 104
- November 2021, AS Paper 2 Statistics, Q3 (5 marks): The random variable X has a discrete uniform distribution and takes values 1, 2, 3, …, n The mean of X is 8 3 (a) Show that n = 15 [2 marks] 3 (b) Find P(X > 4)
- November 2021, AS Paper 2 Statistics, Q5 (5 marks): In a game it is known that: * 25% of players score 0 * 30% of players score 5 * 35% of players score 10 * 10% of players score 20 Players receive prize money, i
- November 2020, Paper 3 Statistics, Q4 (9 marks): The discrete random variable X follows a discrete uniform distribution and takes values 1, 2, 3, …, n. The discrete random variable Y is defined by Y = 2X 4 (a)
- 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, Q1 (1 mark): The discrete random variable X has the following probability distribution function. P(X = x) = 0:2 x = 1 0:3 x = 2 0:1 x = 3, 4 0:25 x = 5 0:05 x = 6 0 otherwis
- November 2020, AS Paper 2 Statistics, Q3 (5 marks): The random variable X represents the value on the upper face of an eight-sided dice after it has been rolled. The faces are numbered 1 to 8 The random variable
- 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
- June 2019, Paper 3 Statistics, Q1 (1 mark): The discrete random variable X has Var (X) = 5 Find Var (4X − 3) Circle your answer. [1 mark] 17 20 77 80
- June 2019, AS Paper 2 Statistics, Q1 (1 mark): The discrete random variable X has the following probability distribution function P(X = x) = 5 − x 10 x = 1, 2, 3, 4 0 otherwise 8 > < > : Find P(X × 3) Circle
- June 2019, AS Paper 2 Statistics, Q5 (9 marks): The discrete random variable X has the following probability distribution function P(X = x) = 1 n x = 1, 2, ..., n 0 otherwise 8 > < > : 5 (a) (i) Prove that E(
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