plumiDiscrete random variables: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 1.1 Discrete random variables, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 29 questions on Discrete random variables, as a list
- June 2025, Statistics Major, Q10 (13 marks): Two independent random variables, X and Y, have distributions B(6, 0.4) and B(3, 0.4) respectively. The random variable T X ( Y Y ) where Y1 and Y2 are two inde
- June 2025, Statistics Major, Q12 (6 marks): The random variable X takes the value 1 with probability p and the value 0 with probability 1 - p. You are given that E(X ) = p and Var(X ) = p - p2. The random
- June 2025, Statistics Minor, Q7 (12 marks): The probability function of the discrete random variable, X, is shown in the table. You are given that a, b and c are constants. x –1 0 1 P X ( x ) = a b c (a)
- June 2025, AS Statistics A, Q2 (7 marks): The probability distribution of a discrete random variable X is given in the table. x 0 1 2 3 1 1 1 P ( X x ) a = 6 3 10 (a) Find the value of a. [1] The probab
- June 2025, AS Statistics A, Q3 (10 marks): The discrete random variable Q has the distribution Geo(0.3). (a) Find ( P Q 2 ) . [1] = (b) Determine ( P Q 5 ) . [2] G The discrete random variable R has a un
- June 2025, AS Statistics A, Q6 (10 marks): The number of misprints in every 100 000 words of a book is denoted by the random variable X. The probability of any given word being misprinted is 0.000 11. Yo
- June 2024, Statistics Major, Q1 (5 marks): The number of insurance policy sales made per month by a salesperson is modelled by the random variable X, with probability distribution shown in the table. r 0
- June 2024, Statistics Minor, Q6 (9 marks): The probability distribution of a discrete random variable, X, is shown in the table below. x 0 1 2 P(X = x) 1 - a - b a b (a) Find E(X) in terms of a and b. [1
- June 2024, AS Statistics A, Q1 (7 marks): The probability distribution for a discrete random variable X is given in the table below. x 0 1 2 3 P ( X x ) 2c 3c 0 5 - . c c = (a) Find the value of c. [2]
- June 2024, AS Statistics A, Q2 (9 marks): In a game of chance there are 32 slots, numbered 1 to 32, and on each turn a ball lands in one of them. You may assume that the process is completely random. Yo
- June 2023, Statistics Major, Q11 (9 marks): The random variable X takes the value 1 with probability p and the value 0 with probability 1 - . p (a) Find each of the following. • E(X) • Var(X) [3] 2 (b) Th
- June 2023, Statistics Minor, Q3 (10 marks): A fair four-sided dice has its faces numbered 0, 1, 2, 3. The dice is rolled three times. The discrete random variable X is the sum of the lowest and highest sc
- June 2023, Statistics Minor, Q7 (6 marks): The discrete random variable X has a uniform distribution over the set of all integers between 100 and n inclusive, where n is a positive integer with n 2 100.
- June 2023, AS Statistics A, Q1 (12 marks): Ryan has 6 one-pound coins and 4 two-pound coins. Ryan decides to select 3 of these coins at random to donate to a charity. The total value, in pounds, of these
- June 2022, Statistics Major, Q3 (6 marks): The table shows the probability distribution of the random variable X, where a and b are constants. r 0 1 2 3 4 a b b2 P(X = r) 0.24 0.32 (a) Given that E(X ) =
- June 2022, Statistics Minor, Q1 (6 marks): In a quiz a contestant is asked up to four questions. The contestant’s turn ends once the contestant gets a question wrong or has answered all four questions. T
- June 2022, AS Statistics A, Q1 (6 marks): A fair five-sided spinner has sectors labelled 1, 2, 3, 4, 5. In a game at a stall at a charity event, the spinner is spun twice. The random variable X represen
- November 2021, Statistics Major, Q2 (13 marks): In a game at a charity fair, a player rolls 3 unbiased six-sided dice. The random variable X represents the difference between the highest and lowest scores. 1
- November 2021, Statistics Minor, Q1 (7 marks): The probability distribution of a discrete random variable X is given by the formula ^ h for r = 1, 2, 3, 4, 5. 2 P ( X r ) k r ( 1 ) 1 = = - + 1 (a) Show that
- November 2021, AS Statistics A, Q1 (4 marks): The random variable X represents the clutch size (the number of eggs laid) by female birds of a particular species. The probability distribution of X is given i
- November 2020, Statistics Major, Q1 (9 marks): In a game at a fair, players choose 4 countries from a list of 10 countries. The names of all 10 countries are then put in a box and the player selects 4 of the
- November 2020, Statistics Minor, Q1 (5 marks): A quiz team of 4 students is to be selected from a group of 7 girls and 5 boys. The team is selected at random from the students in the group. The number of gir
- November 2020, AS Statistics A, Q1 (12 marks): The random variable X represents the number of cars arriving at a car wash per 10-minute period. From observations over a number of days, an estimate was made o
- November 2020, AS Statistics A, Q4 (8 marks): A fair 8-sided dice has faces labelled 1, 2, …, 8. The random variable X represents the score when the dice is rolled once. (a) State the distribution of X. [2]
- June 2019, Statistics Major, Q1 (11 marks): A fair six-sided dice is rolled three times. The random variable X represents the lowest of the three scores. The probability distribution of X is given by the
- June 2019, Statistics Minor, Q1 (7 marks): In a game at a charity fair, a spinner is spun 4 times. On each spin the chance that the spinner lands on a score of 5 is 0.2. The random variable X represents
- June 2019, AS Statistics A, Q1 (8 marks): The discrete random variable X has probability distribution defined by P(X = r) = k(r2 + 3r) for r = 1, 2, 3, 4, 5, where k is a constant. (a) Complete the tabl
- June 2019, AS Statistics B, Q2 (8 marks): Leila and Caleb are playing a game, using fair six‑sided dice and unbiased coins. • Leila rolls two dice, and her score L is the total of the scores on the two
- June 2018, AS Statistics A, Q2 (10 marks): In a quiz, competitors have to match 5 landmarks to the 5 British counties which the landmarks are in. The random variable X represents the number of correct ma
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