SA6-SA7 Discrete uniform distribution Quiz: AQA Further Maths, Unit 4

The 20 questions

1. For a discrete uniform distribution on the set {1, 2, ..., n}, what is P(X = x)?

   • 1/(n + 1)
   • x/n
   • 1/n squared
   • 1/n

2. What is the mean of a discrete uniform distribution on {1, 2, ..., n}?

   • n(n + 1)/2
   • (n - 1)/2
   • (n + 1)/2
   • n/2

3. What is the variance of a discrete uniform distribution on {1, 2, ..., n}?

   • (n^2 - 1)/12
   • n^2/12
   • (n - 1)/12
   • (n^2 + 1)/12

4. When is a discrete uniform distribution a suitable model for a situation?

   • When outcomes are continuous and lie in an interval
   • When the number of trials is large and fixed
   • When larger values are more likely than smaller ones
   • When each of n consecutive integer outcomes is equally likely

5. Which result is used to prove the mean of the discrete uniform distribution?

   • The sum of the first n odd integers is n(n + 1)
   • The sum of the first n positive integers is n^2
   • The sum of the first n positive integers is n(n + 1)/2
   • The product of the first n positive integers is n squared

6. What is the sum of the squares of the first n positive integers?

   • n(n + 1)(n + 2)/3
   • n(n + 1)/2
   • n(n + 1)(2n + 1)/6
   • n^3

7. What is the standard deviation of a discrete uniform distribution on {1, 2, ..., n}?

   • (n - 1)/sqrt(12)
   • sqrt(n/12)
   • (n^2 - 1)/12
   • sqrt((n^2 - 1)/12)

8. A fair six-sided die is rolled. What is the mean of the score?

   • 3.25
   • 4
   • 3
   • 3.5

9. A fair six-sided die is rolled. What is the variance of the score?

   • 35/6
   • 2.5
   • 91/6
   • 35/12

10. A fair ten-sided die numbered 1 to 10 is rolled. What is the variance of the score?

    • 8.25
    • 10
    • 8.5
    • 9.25

11. A discrete uniform random variable X takes values 1 to 20 equally likely. What is P(X = 4)?

    • 0.05
    • 0.2
    • 0.04
    • 0.25

12. A discrete uniform random variable X takes values 1 to 20 equally likely. What is P(X <= 5)?

    • 0.25
    • 0.05
    • 0.3
    • 0.5

13. A lottery draw picks one number from 1 to 49 with each number equally likely. What is the probability of a particular number being drawn?

    • 1/50
    • 1/49
    • 1/48
    • 1/7

14. A discrete uniform distribution on {1, ..., 7} has what variance?

    • 3.5
    • 4.5
    • 8
    • 4

15. A discrete uniform random variable X takes values 1 to n. Its variance is 2. What is n?

    • 6
    • 5
    • 4
    • 25

16. A discrete uniform random variable takes integer values 10 to 20 inclusive, each equally likely. What is its mean?

    • 16
    • 11
    • 14.5
    • 15

17. A discrete uniform distribution on {1, 2, ..., n} has mean 7.5. What is n?

    • 12
    • 7
    • 14
    • 15

18. A discrete uniform random variable X on {1, ..., 6} is used to define Y = 2X + 3. What is E(Y)?

    • 7.5
    • 6.5
    • 13
    • 10

19. A discrete uniform random variable X takes values 1 to 6. What is P(X >= 4)?

    • 0.4
    • 0.5
    • 1/3
    • 0.6

20. A discrete uniform random variable X takes values 1 to n with n = 10. What is its standard deviation, to 3 significant figures?

    • 3.00
    • 2.87
    • 2.50
    • 8.25

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