Lesson SF3-SF4

SF3-SF4 Mean and variance, and the link to Poisson events Quiz: AQA Further Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson SF3-SF4, Mean and variance, and the link to Poisson events: 20 multiple choice questions for the AQA Further Maths (7367), Unit 4: Optional application 2: statistics, written with Revision Ninja.

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The 20 questions

  1. For an exponential distribution with rate lambda, what is E(X)?

    • lambda squared
    • 1/lambda
    • lambda
    • 1/lambda squared

  2. For an exponential distribution with rate lambda, what is Var(X)?

    • 1/lambda
    • 1/lambda squared
    • 2/lambda squared
    • lambda squared

  3. For an exponential distribution with rate lambda, what is the standard deviation of X?

    • lambda
    • sqrt(lambda)
    • 1/sqrt(lambda)
    • 1/lambda

  4. For an exponential distribution with parameter lambda, how do the mean and standard deviation compare?

    • Mean is larger
    • They are equal
    • Mean is zero
    • Standard deviation larger

  5. What distribution models the time between events in a Poisson process with rate lambda?

    • Normal mean lambda
    • Exponential rate lambda
    • Poisson rate lambda
    • Uniform on lambda

  6. What integrand is evaluated from 0 to infinity to find the exponential mean?

    • x lambda e^(-lambda x)
    • x^2 lambda e^(-lambda x)
    • lambda e^(-lambda x)
    • e^(-lambda x)

  7. For a Poisson process with rate lambda, what is the parameter of the exponential distribution of the interval between events?

    • lambda squared
    • 1/lambda
    • 2 lambda
    • lambda

  8. Events occur at 4 per hour, modelled as a Poisson process. What is the mean time between events?

    • 15 minutes
    • 60 minutes
    • 4 minutes
    • 0.4 hours

  9. For an exponential distribution with rate lambda = 0.5, what is the mean?

    • 0.25
    • 2
    • 4
    • 0.5

  10. For an exponential distribution with rate lambda = 0.5, what is the variance?

    • 4
    • 0.5
    • 0.25
    • 2

  11. Events occur at a rate of 3 per minute, modelled as a Poisson process. What is P(the first interval is less than 20 seconds), to 4 decimal places?

    • 0.9502
    • 0.3679
    • 0.6321
    • 0.0498

  12. Events occur at 6 per hour, modelled as a Poisson process. What is the probability of no event in 10 minutes, to 4 decimal places?

    • 0.3679
    • 0.9502
    • 0.6321
    • 0.0498

  13. For an exponential distribution with rate lambda = 0.8, what is the mean?

    • 1.25
    • 0.8
    • 1.6
    • 0.64

  14. For an exponential distribution with rate lambda = 5, what is the standard deviation?

    • 0.04
    • 0.2
    • 5
    • 25

  15. Events occur at a rate of 2 per minute, modelled as a Poisson process. What is the probability that an interval between events exceeds 1 minute, to 4 decimal places?

    • 0.3679
    • 0.8647
    • 0.1353
    • 0.6321

  16. Events occur as a Poisson process at rate 4 per hour. What is the probability that the next event occurs within 30 minutes, to 4 decimal places?

    • 0.6321
    • 0.1353
    • 0.8647
    • 0.3679

  17. Which integration technique is used to evaluate the integral of x lambda e^(-lambda x)?

    • Integration by substitution
    • Trapezium rule
    • Integration by parts
    • Partial fractions

  18. For an exponential distribution, what is E(X^2)?

    • 2/lambda squared
    • 1/lambda squared
    • lambda squared / 2
    • 2/lambda

  19. For an exponential distribution with rate lambda, what is the value of lambda if the mean is 5 minutes?

    • 0.05
    • 0.2
    • 0.5
    • 5

  20. An exponential distribution has rate lambda = 0.5 per minute. What is P(X > mean), to 4 decimal places?

    • 0.5000
    • 0.3679
    • 0.1353
    • 0.6321

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