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Mean and SD of the inverse of a population

  1. Jun 23, 2013 #1
    If one has the mean and standard deviation of a population, is it possible to calculate (or estimate) the mean and standard deviation of the inverse population (ie. 1/(every value in the original population)?

    Thank you!
  2. jcsd
  3. Jun 23, 2013 #2


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    Can't you use :

    E(g(X))=∫g(x)f(x)dx ,

    where f(x) is the p.d.f of X?

    I don't know if you know just the values E(X) and σ(X), or if you got those using the known
    value f(x).
  4. Jun 27, 2013 #3


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    No, it's not possible on those data alone. You might be able to derive some bounds if you know a bit more, like a minimum value for X > 0.
  5. Jun 28, 2013 #4

    Stephen Tashi

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    Clarify what you mean by "population". Do you mean a statistical distribution from a known family of distributions, like a "normal distribution"? Or do you mean the mean and standard deviation computed from a collection of data that comes from an unknown probability distribution ( like the "mean height of all emergency personnel in the city") ?
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