Lesson 5.02f-i

5.02f-i Geometric and Poisson distributions Quiz: OCR Further Maths, Unit 2

20 questions

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Lesson 5.02f-i, Geometric and Poisson distributions: 20 multiple choice questions for the OCR Further Maths (H245), Unit 2: Statistics (Y542), written with Revision Ninja.

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The 20 questions

  1. What parameter defines a Geometric distribution X ~ Geo(p)?

    • Sample variance
    • Number of trials
    • Mean rate
    • Probability of success
  2. What is the formula for P(X = r) for X ~ Geo(p), where q = 1 - p?

    • q^r p
    • q^(r-1) p
    • (1-p)^r
    • p^r q
  3. What is the expected value E(X) of a random variable X ~ Geo(p)?

    • 1 - p
    • 1 / p
    • (1-p) / p
    • p
  4. What is the variance Var(X) of a random variable X ~ Geo(p), where q = 1 - p?

    • 1 / p^2
    • q / p
    • q / p^2
    • p / q^2
  5. What is the simplified expression for P(X > r) when X ~ Geo(p) and q = 1 - p?

    • q^(r-1)
    • 1 - q^r
    • p^r
    • q^r
  6. Which parameter defines a Poisson distribution X ~ Po(lambda)?

    • Number of trials
    • Mean rate
    • Probability of success
    • Sample variance
  7. For a Poisson distribution X ~ Po(lambda), how do the mean and variance compare?

    • They are equal
    • Sum equals one
    • Variance is larger
    • Mean is larger
  8. What is the probability mass function formula for P(X = 0) in X ~ Po(lambda)?

    • e^lambda
    • 1 - e^(-lambda)
    • lambda e^(-lambda)
    • e^(-lambda)
  9. If X ~ Geo(0.2), what is the expected value E(X)?

    • 2
    • 0.2
    • 0.8
    • 5
  10. If X ~ Geo(0.1), what is the probability P(X > 2)?

    • 0.81
    • 0.01
    • 0.19
    • 0.09
  11. If X ~ Geo(0.5), what is the exact value of P(X = 3)?

    • 0.125
    • 0.375
    • 0.25
    • 0.5
  12. If X ~ Po(2) and Y ~ Po(3) are independent, what distribution does X + Y follow?

    • Po(2.5)
    • Po(5)
    • Po(1)
    • Po(6)
  13. Calls arrive at 4 per hour. What is the mean number of calls in 30 minutes?

    • 12
    • 8
    • 4
    • 2
  14. A Poisson random variable has a variance of 9. What is its mean?

    • 4.5
    • 81
    • 3
    • 9
  15. What is the mode of any Geometric distribution X ~ Geo(p)?

    • 0
    • 1
    • p
    • 1/p
  16. If X ~ Po(3), what is the formula expression for P(X = 1)?

    • 3 e^(-3)
    • e^(-3)
    • 9 e^(-3)
    • 1.5 e^(-3)
  17. Which property states that P(X > s + t | X > s) = P(X > t)?

    • Symmetry property
    • Additive property
    • Memoryless property
    • Scaling property
  18. Under what conditions does Bin(n, p) approximate to a Poisson distribution Po(lambda)?

    • Small n, small p
    • Small n, large p
    • Large n, small p
    • Large n, p = 0.5
  19. Which assumption is essential for modelling events with a Poisson distribution?

    • Probabilities change
    • Events occur independently
    • Fixed trial number
    • Two outcomes only
  20. For X ~ Geo(0.4), what is the value of P(X <= 2)?

    • 0.36
    • 0.64
    • 0.84
    • 0.16

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