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

The 20 questions

1. What is multiplied by f(x) inside the integral to find E(X)?

   • F(x)
   • x^2
   • 1
   • 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. How is the mode of a continuous random variable identified from its pdf f(x)?

   • Root of f(x)
   • Peak of f(x)
   • Minimum of f(x)
   • Mean of X

4. What value of the cumulative distribution function equals the median of a continuous random variable?

   • 0.5
   • 1.0
   • 0.25
   • 0.0

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. What is the relationship between mean and median for a negatively skewed distribution?

   • Mean < median
   • Mean > median
   • Mean = 0
   • Mean = 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. What is the skewness of a continuous random variable with pdf f(x) = 2x on [0, 1]?

    • Zero
    • Negative
    • Undefined
    • Positive

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. What skewness is indicated when the mean is greater than the median and mode?

    • Positive skew
    • Zero skew
    • Symmetrical
    • Negative skew

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