Probability distributions, expectation and variance

  • Binomial or not?
    problem

    Binomial or not?

    Age
    16 to 18
    Challenge level
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    Are these scenarios described by the binomial distribution?
  • Aim high
    problem

    Aim high

    Age
    16 to 18
    Challenge level
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    How do you choose your planting levels to minimise the total loss at harvest time?
  • Binomial conditions
    problem

    Binomial conditions

    Age
    16 to 18
    Challenge level
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    When is an experiment described by the binomial distribution? Why do we need both the condition about independence and the one about constant probability?
  • A well-stirred sample
    problem

    A well-stirred sample

    Age
    16 to 18
    Challenge level
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    Typical survey sample sizes are about 1000 people. Why is this?
  • Random inequalities
    problem

    Random inequalities

    Age
    16 to 18
    Challenge level
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    Can you build a distribution with the maximum theoretical spread?
  • Time to evolve 2
    problem

    Time to evolve 2

    Age
    16 to 18
    Challenge level
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    How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?