Discrete random variables: Edexcel International A Level Further Maths questions

Every Edexcel International A Level Further Maths exam question on S1.5 Discrete random variables, 2019–2025, with its mark scheme and examiner’s report.

All 19 questions on Discrete random variables, as a list

June 2025, AS Statistics 1 (S1), Q1 (9 marks): The discrete random variable X has probability distribution x 1 2 3 4 P(X = x) 0.3 0.2 0.35 0.15 (a) Find F(3.5) (b) Find P(3X – 3 < X + 2) (c) Find E(X) (d) Sh
January 2025, AS Statistics 1 (S1), Q1 (15 marks): Jen has one fair 4-sided red die and one fair 4-sided blue die. • The red die has sides numbered 1, 2, 3 and 4 • The blue die has sides numbered 1, 3, 5 and 7 T
October 2024, AS Statistics 1 (S1), Q6 (14 marks): A biased die with six faces is rolled. The discrete random variable X represents the score which is uppermost. The cumulative distribution function of X is show
June 2024, AS Statistics 1 (S1), Q2 (12 marks): A spinner can land on the numbers 2, 4, 5, 7 or 8 only. The random variable X represents the number that this spinner lands on when it is spun once. The probabi
January 2024, AS Statistics 1 (S1), Q7 (10 marks): The cumulative distribution of a discrete random variable X is given by x 1 2 3 4 F(x) 1 13 2 1 26 k − 3 1 26 k k + 4 8 where k is a positive constant. (a) Show
October 2023, AS Statistics 1 (S1), Q4 (12 marks): The discrete random variable X has the following probability distribution. x 1 2 3 4 P(X = x) 1 10 1 5 3 10 2 5 (a) Show that E 1 2 5 X (b) Find Var 1 X
June 2023, AS Statistics 1 (S1), Q5 (13 marks): A discrete random variable Y has probability function P( ) ( ) ( ) Y y k y k y k 3 8 0 2 y = 1, 2 y = 3, 4, 5 y = 6 otherwise where k is a constant. (a) Show th
January 2023, AS Statistics 1 (S1), Q3 (11 marks): The probability distribution of the discrete random variable X is given by x 2 3 4 P(X = x) a 0.4 0.6 – a where a is a constant. (a) Find, in terms of a, E(X) (
October 2022, AS Statistics 1 (S1), Q4 (4 marks): The cumulative distribution function of the discrete random variable W, which takes only the values 6, 7 and 8, is given by F(W ) = ( )( ) w w + − 3 1 77 for w
October 2022, AS Statistics 1 (S1), Q7 (14 marks): Adana selects one number at random from the distribution of X which has the following probability distribution. x 0 5 10 P(X = x) 0.1 0.2 0.7 (a) Given that the
June 2022, AS Statistics 1 (S1), Q5 (14 marks): A red spinner is designed so that the score R is given by the following probability distribution. r 2 3 4 5 6 P(R = r) 0.25 0.3 0.15 0.1 0.2 (a) Show that E(R2)
January 2022, AS Statistics 1 (S1), Q4 (13 marks): The random variable W has a discrete uniform distribution where P(W = w) = 1 5 for w = 1, 2, 3, 4, 5 (a) Find P(2  W < 3.5) The discrete random variable X = 5
January 2022, AS Statistics 1 (S1), Q7 (11 marks): A bag contains n marbles of which 7 are green. From the bag, 3 marbles are selected at random. The random variable X represents the number of green marbles sele
October 2021, AS Statistics 1 (S1), Q4 (13 marks): Three bags A, B and C each contain coloured balls. Bag A contains 4 red balls and 2 yellow balls only. Bag B contains 4 red balls and 1 yellow ball only. Bag C
October 2021, AS Statistics 1 (S1), Q5 (14 marks): The discrete random variable Y has the following probability distribution y − 9 − 5 0 5 9 P(Y = y) q r u r q where q, r and u are probabilities. (a) Write down
June 2021, AS Statistics 1 (S1), Q5 (15 marks): The discrete random variable X has the following probability distribution x −2 −1 0 1 4 P(X = x) a b c b a Given that E(X ) = 0.5 (a) find the value of a. Given
January 2021, AS Statistics 1 (S1), Q4 (16 marks): A spinner can land on the numbers 10, 12, 14 and 16 only and the probability of the spinner landing on each number is the same. The random variable X represents
October 2020, AS Statistics 1 (S1), Q1 (5 marks): The discrete random variable X takes the values −1, 2, 3, 4 and 7 only. Given that P(X = x) = 8 −x k for x = −1, 2, 3, 4 and 7 find the value of E(X )
October 2020, AS Statistics 1 (S1), Q6 (15 marks): The random variable A represents the score when a spinner is spun. The probability distribution for A is given in the following table. a 1 4 5 7 P(A = a) 0.40 0

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