Lesson 3B.2.1

3B.2.1 The Poisson distribution Quiz: Pearson Edexcel Further Maths, Unit 11

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 3B.2.1, The Poisson distribution: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 11: Poisson and binomial distributions, written with Revision Ninja.

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The 20 questions

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

    • P(X = x) = e^(-lambda) lambda^x / x! for x = 0, 1, 2, ...
    • P(X = x) = lambda e^(-x) / x! for x = 0, 1, 2, ...
    • P(X = x) = e^(-lambda) x^lambda / lambda! for x = 0, 1, 2, ...
    • P(X = x) = lambda^x e^(lambda) / x! for x = 0, 1, 2, ...

  2. What are the mean and variance of a Poisson distribution with parameter lambda?

    • Both are lambda
    • Mean lambda and variance lambda^2
    • Mean lambda^2 and variance lambda
    • Both are 1/lambda

  3. If X ~ Po(lambda) and Y ~ Po(mu) are independent, what is the distribution of X + Y?

    • Po(lambda mu)
    • Po(lambda - mu)
    • Po(lambda + mu + 1)
    • Po(lambda + mu)

  4. Which conditions justify modelling a count with a Poisson distribution?

    • Events occur singly, randomly, independently and at a constant average rate
    • Events occur only in pairs, always at exactly the same moment in time
    • The average rate changes every hour and events depend on earlier events
    • The number of trials is fixed in advance and each trial has probability 0.5

  5. If the number of events per minute is Po(lambda), what is the distribution of the number of events in 5 minutes?

    • Po(5 lambda)
    • Po(lambda)
    • Po(lambda^5)
    • Po(lambda / 5)

  6. If X ~ Po(3), what is P(X = 0) to 4 decimal places?

    • 0.9502
    • 0.0498
    • 20.0855
    • 0.1494

  7. If X ~ Po(2), what is P(X = 2) to 4 decimal places?

    • 0.2707
    • 0.6767
    • 0.5413
    • 0.1353

  8. If X ~ Po(1.5), what is P(X <= 1) to 4 decimal places?

    • 0.2231
    • 0.5578
    • 0.3347
    • 0.7769

  9. If X ~ Po(4), what is P(X >= 1) to 4 decimal places?

    • 0.5000
    • 0.9817
    • 0.0183
    • 0.0733

  10. X ~ Po(2) and Y ~ Po(3) are independent. What is P(X + Y = 0) to 4 decimal places?

    • 0.0337
    • 0.0025
    • 0.0067
    • 0.3679

  11. Calls to a help line follow Po(6) per hour. What is the expected number of calls in 15 minutes?

    • 2.5
    • 1.5
    • 0.4
    • 6

  12. If X ~ Po(lambda) and P(X = 1) = P(X = 2), what is lambda?

    • 3
    • 4
    • 1
    • 2

  13. If X ~ Po(2), what is P(X = 3 | X >= 1) to 3 decimal places?

    • 0.209
    • 0.135
    • 0.271
    • 0.181

  14. If X ~ Po(lambda) and P(X = 0) = 0.2, what is lambda?

    • ln 5, about 1.609
    • 5
    • 0.2
    • ln 0.2, about -1.609

  15. A call centre receives 4 calls per 10 minutes on average, modelled as Poisson. What is the probability of no calls in 5 minutes, to 3 decimal places?

    • 0.018
    • 0.368
    • 0.135
    • 0.271

  16. X1, X2 and X3 are independent, each Po(2). What is P(X1 + X2 + X3 = 6) to 4 decimal places?

    • 0.0900
    • 0.0025
    • 0.1606
    • 0.4463

  17. Which condition is needed for X + Y to be Poisson with parameter lambda + mu?

    • X and Y have equal means
    • X and Y are identically distributed
    • X and Y are independent
    • X and Y are both binomial

  18. Which situation is best modelled by a Poisson distribution?

    • Number of cards of a given suit in a fixed deck
    • Number of heads in 10 fixed coin tosses
    • Number of emails arriving at a server in an hour
    • Number of students in a class of 30

  19. If X ~ Po(2), what is E(X^2)?

    • 2
    • 8
    • 6
    • 4

  20. If X ~ Po(3), what is P(X = 0) + P(X = 1) to 4 decimal places?

    • 0.1991
    • 0.4232
    • 0.0498
    • 0.1494

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