SD1-SD3 Probability density functions, medians and quartiles Quiz: AQA Further Maths, Unit 4

The 20 questions

1. What is the total area under a valid probability density function?

   • 1
   • 0.5
   • 0
   • Infinity

2. What feature of a probability density function f(x) between a and b gives P(a ≤ X ≤ b)?

   • x-intercept
   • Peak value
   • Gradient of f(x)
   • Area under f(x)

3. What is the probability that a continuous random variable takes a single exact value?

   • 0
   • f(a)
   • 0.5
   • 1

4. What does the value of a probability density function f(x) at point x represent?

   • Expected value
   • Cumulative probability
   • Probability density
   • Exact probability

5. For a continuous random variable X with median m, what is P(X ≤ m)?

   • 0.25
   • 0.5
   • 0
   • 0.75

6. What is the cumulative probability P(X ≤ Q1) for the lower quartile Q1?

   • 0.25
   • 0.5
   • 0.75
   • 0.1

7. A continuous random variable has pdf f(x) = 2x for 0 <= x <= 1 and zero otherwise. What is P(0.2 <= X <= 0.5)?

   • 0.25
   • 0.04
   • 0.21
   • 0.30

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

   • sqrt(0.5), about 0.707
   • 0.25
   • 0.5
   • 0.75

9. For the pdf f(x) = 2x on [0, 1], what is the lower quartile Q1?

   • 0.75
   • sqrt(0.5), about 0.707
   • 0.25
   • 0.5

10. For the pdf f(x) = 2x on [0, 1], what is the upper quartile Q3?

    • 0.707
    • 0.75
    • 0.6
    • 0.866

11. What value of k makes f(x) = kx on [0, 2] (zero elsewhere) a valid pdf?

    • 0.5
    • 2
    • 0.25
    • 1

12. A continuous random variable has pdf f(x) = 3x^2 on [0, 1]. What is P(X <= 0.5)?

    • 0.375
    • 0.5
    • 0.25
    • 0.125

13. A continuous random variable has pdf f(x) = 1/4 on [0, 4] and zero elsewhere. What is its median?

    • 1
    • 2
    • 2.5
    • 4

14. A continuous random variable has pdf f(x) = 2(1 - x) on [0, 1]. What is P(X >= 0.5)?

    • 0.25
    • 0.125
    • 0.75
    • 0.5

15. A continuous random variable has pdf f(x) = 2x on [0, 1]. What is P(X > 0.9)?

    • 0.81
    • 0.1
    • 0.19
    • 0.9

16. A continuous random variable has pdf f(x) = k(4 - x) on [0, 4] and zero elsewhere. What is k?

    • 1/8
    • 1/4
    • 1/2
    • 1/16

17. A continuous random variable has pdf f(x) = k x^2 on [0, 3] and zero elsewhere. What is P(X <= 1)?

    • 1/9
    • 1/3
    • 1/81
    • 1/27

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

    • about 0.794
    • 0.5
    • about 0.707
    • 1/3

19. A continuous random variable has pdf f(x) = x on [0, 1] and f(x) = 2 - x on [1, 2], zero elsewhere. What is P(X <= 1)?

    • 0.5
    • 1
    • 0.25
    • 0.75

20. What is the median of a continuous random variable symmetric on the interval [0, 2]?

    • 2
    • 0.5
    • 0
    • 1

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