2.04a Simple finite discrete distributions Quiz: OCR Maths, Unit 14

The 20 questions

1. What must the sum of all probabilities in a discrete probability distribution equal?

   • 0
   • 1
   • 0.5
   • Infinity

2. What is the formula for the mean of a binomial distribution X ~ B(n, p)?

   • npq
   • np
   • p/n
   • n(1 - p)

3. What is the formula for the variance of a binomial distribution X ~ B(n, p)?

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

4. In the notation X ~ B(10, 0.3), what does the number 10 represent?

   • Expected value
   • Probability of success
   • Variance
   • Number of trials

5. Which condition is required for a variable to follow a binomial distribution?

   • Constant success probability
   • Variable trial count
   • Dependent trials
   • Continuous outcomes

6. A discrete random variable X has P(X=x) = kx for x = 1, 2, 3. What is k?

   • 1/2
   • 1/5
   • 1/3
   • 1/6

7. If X ~ B(5, 0.2), what is the mean of X?

   • 1
   • 0.2
   • 0.8
   • 5

8. If X ~ B(10, 0.4), what is the variance of X?

   • 0.24
   • 4
   • 1.6
   • 2.4

9. What is the value of P(X = 0) for a binomial variable X ~ B(n, p)?

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

10. What is the value of P(X = n) for a binomial variable X ~ B(n, p)?

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

11. If X ~ B(4, 0.5), what is the probability that X = 4?

    • 0.125
    • 0.25
    • 0.0625
    • 0.5

12. How is P(X >= 1) calculated using the complement rule for a discrete variable?

    • 1 - P(X = 0)
    • 1 + P(X = 0)
    • P(X = 0)
    • 1 - P(X = 1)

13. Which term describes a random variable that takes only distinct, countable values?

    • Discrete
    • Normal
    • Continuous
    • Uniform

14. In binomial probability formulas, what does the quantity q represent?

    • 1 / p
    • p^2
    • 1 + p
    • 1 - p

15. A discrete variable X takes values 1 and 2, with P(X=1) = 0.3. What is P(X=2)?

    • 0.7
    • 0.4
    • 0.5
    • 0.3

16. Which probability expression represents obtaining no more than x successes?

    • P(X < x)
    • P(X <= x)
    • P(X = x)
    • P(X >= x)

17. Why is flipping a biased coin 10 times modelled by a binomial distribution?

    • Infinite trials
    • Continuous outcomes
    • Variable probabilities
    • Independent trials

18. If X ~ B(3, 0.1), what is the value of P(X = 0)?

    • 0.9
    • 0.27
    • 0.001
    • 0.729

19. What is the valid range for any individual probability in a discrete distribution?

    • -1 to 1
    • 0 to infinity
    • 0 to 1 inclusive
    • Greater than 1

20. If a binomial distribution X ~ B(n, p) has mean 12 and p = 0.4, what is n?

    • 30
    • 15
    • 4.8
    • 20

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