Lesson 3B.3.1

3B.3.1 Geometric and negative binomial models Quiz: Pearson Edexcel Further Maths, Unit 12

20 questions

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Lesson 3B.3.1, Geometric and negative binomial models: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 12: Geometric and negative binomial distributions, written with Revision Ninja.

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The 20 questions

  1. What is the probability mass function of a geometric random variable X with parameter p?

    • P(X = x) = p^x (1 - p)^(x - 1)
    • P(X = x) = p(1 - p)^x for x = 0, 1, 2, ...
    • P(X = x) = (1 - p)p^(x - 1)
    • P(X = x) = p(1 - p)^(x - 1) for x = 1, 2, 3, ...

  2. What does a Geometric random variable X ~ Geo(p) count in Pearson statistics?

    • Successes in fixed trials
    • Trials until first success
    • Trials until r successes
    • Failures before first success

  3. What does a Negative Binomial random variable X ~ NegBin(r, p) count?

    • Failures until r successes
    • Trials until r successes
    • Trials until first success
    • Successes in r trials

  4. For a Negative Binomial variable X ~ NegBin(r, p), what is the minimum value X can take?

    • r - 1
    • 0
    • r
    • 1

  5. What is the special case of the negative binomial distribution when r = 1?

    • The uniform distribution
    • The binomial distribution
    • The geometric distribution
    • The Poisson distribution

  6. A geometric distribution has p = 0.2. What is P(X = 3)?

    • 0.064
    • 0.128
    • 0.512
    • 0.16

  7. A geometric distribution has p = 0.1. What is P(first success on the 4th trial)?

    • 0.0729
    • 0.6561
    • 0.1000
    • 0.0900

  8. For a geometric distribution with p = 0.25, what is P(X > 3)?

    • 0.1406
    • 0.4219
    • 0.0469
    • 0.5625

  9. A negative binomial distribution has r = 2 and p = 0.3. What is P(X = 3)?

    • 0.063
    • 0.147
    • 0.126
    • 0.189

  10. A negative binomial distribution has r = 3 and p = 0.4. What is P(X = 3)?

    • 0.064
    • 0.096
    • 0.192
    • 0.024

  11. A fair coin is tossed repeatedly. What is the probability that the third head occurs on the fifth toss?

    • 0.1875
    • 0.3125
    • 0.0625
    • 0.25

  12. X ~ NB(r = 3, p = 0.4). What is P(X = 5) to 4 decimal places?

    • 0.2304
    • 0.1382
    • 0.1152
    • 0.0922

  13. A die is rolled until a six appears. What is the probability that more than three rolls are needed?

    • 1/216
    • 91/216
    • 125/216
    • 5/6

  14. A geometric distribution has p = 0.2. What is P(X >= 4)?

    • 0.4096
    • 0.2048
    • 0.512
    • 0.8

  15. X ~ Geo(0.1). What is P(X <= 5) to 4 decimal places?

    • 0.5000
    • 0.5905
    • 0.0590
    • 0.4095

  16. A negative binomial distribution has r = 2 and p = 0.4. What is P(X = 4)?

    • 0.1728
    • 0.0864
    • 0.1152
    • 0.2304

  17. What is the sum of P(X = x) over all x for a geometric distribution?

    • 0
    • 1
    • p
    • 1/p

  18. A fair coin is tossed. What is P(X = 1) for the geometric count of trials to the first head?

    • 1
    • 0.25
    • 0
    • 0.5

  19. What do the parameters r and p represent in a Negative Binomial distribution?

    • Trial count, mean rate
    • Target successes, success probability
    • Mean, standard deviation
    • Success probability, variance

  20. A player tries repeatedly with success probability 0.4 per attempt. What is the probability that the first success occurs on attempt 2 or attempt 3?

    • 0.600
    • 0.384
    • 0.240
    • 0.144

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