Lesson 4B.2.3-4B.2.4

4B.2.3-4B.2.4 Mean and variance of continuous random variables Quiz: Pearson Edexcel Further Maths, Unit 19

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson 4B.2.3-4B.2.4, Mean and variance of continuous random variables: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 19: Continuous random variables, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. Which expression gives the mean E(X) of a continuous random variable with pdf f(x)?

    • The integral of F(x) with respect to x over all x
    • The integral of f(x) with respect to x over all x, which equals 1
    • The integral of x^2 f(x) with respect to x over all x
    • The integral of x f(x) with respect to x over all x

  2. Which expression gives the variance of a continuous random variable X?

    • E(X) minus [E(X)]^2
    • E(X^2) plus [E(X)]^2
    • [E(X)]^2 minus E(X^2)
    • E(X^2) minus [E(X)]^2

  3. What is the mode of a continuous random variable?

    • The average of x weighted by f(x)
    • The value of x at which the pdf f(x) is maximum
    • The value m for which F(m) = 0.5
    • The value of x at which f(x) equals 0

  4. What is the median of a continuous random variable X?

    • The value m such that F(m) = 0.5
    • The value m at which the density f(m) equals 0.5
    • The mean of the middle 50 per cent of the distribution
    • The value of x where F(x) equals 1

  5. For a continuous uniform distribution on [a, b], what is the variance?

    • (b - a)^2 / 4
    • (b - a) / 2
    • (b - a)^2 / 12
    • (a + b)^2 / 12

  6. A distribution is negatively skewed when which relationship holds between the mean and the median?

    • The mean is less than the median
    • The mean is greater than the median
    • The mode is greater than the mean
    • The mean equals the median

  7. If E(X) = 4 and Var(X) = 9, what is E(X^2)?

    • 25
    • 36
    • 13
    • 16

  8. For constants a and b, which expression gives E(aX + b)?

    • a E(X) b
    • a E(X) + b^2
    • a E(X) + b
    • a + b E(X)

  9. A continuous random variable has pdf f(x) = 2x on [0, 1]. What is E(X)?

    • 2/3
    • 1/2
    • 3/4
    • 1/3

  10. A continuous random variable has pdf f(x) = 3x^2 on [0, 1]. What is Var(X)?

    • 3/16
    • 9/16
    • 3/5
    • 3/80

  11. A continuous random variable has E(X) = 3/4 when its pdf is f(x) = 3x^2 on [0, 1]. What is E(3X + 2)?

    • 17/4
    • 9/4
    • 13/4
    • 11/4

  12. A continuous random variable is uniform on [2, 8]. What is its variance?

    • 6
    • 1.5
    • 3
    • 9

  13. A continuous random variable has pdf f(x) = 6x(1 - x) on [0, 1]. What is Var(X)?

    • 0.25
    • 0.05
    • 0.3
    • 0.1

  14. A continuous random variable has pdf f(x) = 2x on [0, 1]. What is E(X^2)?

    • 1/3
    • 1/4
    • 1/2
    • 2/3

  15. A continuous random variable has pdf f(x) = 2x on [0, 1]. Which statement about its skewness is correct?

    • Zero, because the distribution is symmetric about its mean
    • Negative, since the mean 2/3 is below the median of about 0.707
    • Positive, since the median is below the mean
    • Positive, since the mode of 1 lies below the mean

  16. A continuous random variable has pdf f(x) = (3/8) x^2 on [0, 2]. What is E(X)?

    • 3/2
    • 2
    • 6/5
    • 4/3

  17. A continuous random variable has pdf f(x) = (3/8) x^2 on [0, 2]. What is Var(X)?

    • 2.4
    • 0.15
    • 0.4
    • 0.25

  18. A random variable X has Var(X) = 9. Let Y = (X - 4)/3. What is Var(Y)?

    • 3
    • 1/3
    • 1
    • 0

  19. A continuous random variable has pdf f(x) = 2x on [0, 1]. What is its median?

    • 0.667
    • 1/3
    • 0.5
    • 1/sqrt(2), about 0.707

  20. A continuous random variable has mode 2, median 3 and mean 4. Which statement describes its skewness?

    • Positive skew, since the mean is greater than the median
    • Zero skew, since the three measures are different
    • The skewness cannot be determined from these values
    • Negative skew, since the mode is less than the mean

All Pearson Edexcel Further Maths quizzes