5.02d-e Binomial and discrete uniform distributions Quiz: OCR Further Maths, Unit 2

The 20 questions

1. What is the formula for the mean of a discrete uniform distribution on integers 1 to n?

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

2. What is the formula for the variance of a discrete uniform distribution on integers 1 to n?

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

3. What is the expectation formula for a Binomial distribution with parameters n and p?

   • np^2
   • np(1 - p)
   • np
   • n(1 - p)

4. What is the variance formula for a Binomial distribution with parameters n and p?

   • np^2
   • n(1 - p)
   • np
   • np(1 - p)

5. Which condition must hold for trials modelled by a Binomial distribution?

   • Dependent trials
   • Independent trials
   • Varying probabilities
   • Continuous outcomes

6. What is the probability mass function value for each outcome of a discrete uniform distribution U(n)?

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

7. What is the maximum possible value taken by a Binomial random variable X with parameter n?

   • np
   • 1
   • n - 1
   • n

8. What value of parameter p makes a Binomial distribution symmetrical?

   • 1
   • 0.5
   • 0
   • 0.2

9. What is the expectation of a discrete uniform distribution on integers 1 to 6?

   • 3.25
   • 3.5
   • 3
   • 4

10. What is the variance of a discrete uniform distribution on integers 1 to 5?

    • 2.5
    • 3
    • 2
    • 1.5

11. What is the expectation of a Binomial random variable with n = 10 and p = 0.3?

    • 2.1
    • 3
    • 0.3
    • 7

12. What is the variance of a Binomial random variable with n = 20 and p = 0.2?

    • 4
    • 3.2
    • 16
    • 0.8

13. A fair eight-sided die numbered 1 to 8 is rolled. What is the expected score?

    • 5
    • 4.5
    • 4
    • 5.25

14. A fair coin is tossed 4 times. What is the probability of getting exactly 2 heads?

    • 0.25
    • 0.125
    • 0.375
    • 0.5

15. If a discrete uniform variable on 1 to n has mean 6, what is n?

    • 12
    • 11
    • 10
    • 6

16. If a Binomial variable with probability p = 0.4 has mean 8, what is n?

    • 3.2
    • 32
    • 20
    • 12

17. A Binomial variable has mean 6 and variance 2.4. What is the value of p?

    • 0.16
    • 0.6
    • 0.25
    • 0.4

18. If a discrete uniform variable on 1 to n has variance 10, what is n?

    • 9
    • 10
    • 12
    • 11

19. For a Binomial distribution with n = 12 and p = 0.5, what is Var(X)/E(X)?

    • 0.25
    • 3
    • 0.5
    • 1

20. If X is uniformly distributed on consecutive integers from 5 to 11, what is E(X)?

    • 7
    • 8
    • 7.5
    • 8.5

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