SD4-SD5 Mean, variance and linear functions of continuous variables Quiz: AQA Further Maths, Unit 4

The 20 questions

1. For a continuous random variable with pdf f(x), which integral gives E(X)?

   • Integral of x squared f(x) dx
   • Integral of f(x) dx
   • Integral of x f(x) dx
   • Integral of f(x) divided by x dx

2. Which integral gives E(X^2) for a continuous random variable X?

   • Integral of x f(x) dx squared
   • Integral of x squared f(x) dx
   • Integral of 2x f(x) dx
   • Integral of x f(x)^2 dx

3. Which formula gives the variance of a continuous random variable X?

   • Var(X) = E(X^2) + [E(X)]^2
   • Var(X) = [E(X)]^2 - E(X^2)
   • Var(X) = E(X) - [E(X)]^2
   • Var(X) = E(X^2) - [E(X)]^2

4. For constants a and b, what is E(aX + b) for a continuous random variable X?

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

5. For constants a and b, what is Var(aX + b) for a continuous random variable X?

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

6. For a continuous random variable X and a function g, which integral gives E(g(X))?

   • Integral of g(x) dx
   • Integral of x g(x) f(x) dx
   • Integral of g(x) f(x) dx
   • g(E(X))

7. The standard deviation of a continuous random variable is:

   • The variance squared
   • The positive square root of the variance
   • The integral of f(x) squared
   • The variance divided by the mean

8. For the pdf f(x) = 2x on [0, 1], what is E(X)?

   • 3/4
   • 1/3
   • 1/2
   • 2/3

9. For the pdf f(x) = 2x on [0, 1], what is E(X^2)?

   • 1/2
   • 2/3
   • 1/4
   • 1/3

10. For the pdf f(x) = 2x on [0, 1], what is Var(X)?

    • 1/18
    • 1/12
    • 2/9
    • 1/6

11. A continuous random variable X is uniform on [0, 4] with pdf 1/4. What is E(X)?

    • 8/3
    • 2
    • 1
    • 4

12. A continuous random variable X is uniform on [0, 4] with pdf 1/4. What is Var(X)?

    • 1/3
    • 2
    • 16/3
    • 4/3

13. For the pdf f(x) = 2x on [0, 1], what is E(3X + 1)?

    • 3
    • 4
    • 2/3
    • 2

14. For the pdf f(x) = 2x on [0, 1], what is Var(3X + 1)?

    • 1/2
    • 3/2
    • 1/6
    • 1/18

15. For the pdf f(x) = 3x^2 on [0, 1], what is E(X)?

    • 1/2
    • 1
    • 3/4
    • 2/3

16. For the pdf f(x) = 2x on [0, 1], what is the standard deviation of X, to 3 decimal places?

    • 0.333
    • 0.707
    • 0.167
    • 0.236

17. A continuous random variable X is uniform on [0, 4]. Let Y = 2X - 1. What is E(Y)?

    • 1
    • 3
    • 7
    • 5

18. A continuous random variable X is uniform on [0, 4]. Let Y = 2X - 1. What is Var(Y)?

    • 16/3
    • 16
    • 8/3
    • 4/3

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

    • 16/3
    • 4
    • 8/3
    • 16

20. For the pdf f(x) = 2x on [0, 1], what is E(X^3)?

    • 1/2
    • 2/3
    • 2/5
    • 1/3

Related quizzes

• Discrete random variables and their measures Quiz · SA1-SA3 · 20 questions
• Expectation and linear functions Quiz · SA4-SA5 · 20 questions
• Discrete uniform distribution Quiz · SA6-SA7 · 20 questions
• Modelling with the Poisson distribution Quiz · SB1-SB2 · 20 questions
• Mean, variance and sums of Poisson distributions Quiz · SB3-SB4 · 20 questions
• Hypothesis test for a Poisson mean Quiz · SB5 · 20 questions
• Type I and Type II errors and the power of a test · SC1-SC2 · 20 questions
• Probability density functions, medians and quartiles Quiz · SD1-SD3 · 20 questions
• Cumulative distribution functions and the rectangular distribution Quiz · SD6-SD8 · 20 questions
• Contingency tables and expected frequencies Quiz · SE1-SE3 · 20 questions