Mean and SD of the inverse of a population

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SUMMARY

The discussion centers on the feasibility of calculating the mean and standard deviation of the inverse of a population given the mean and standard deviation of the original population. It is established that without additional information about the probability density function (p.d.f) of the original population, such as its distribution type or bounds, it is not possible to derive these statistics for the inverse population. The integral formula E(g(X))=∫g(x)f(x)dx is mentioned as a potential approach, but it requires knowledge of the p.d.f.

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  • Understanding of probability density functions (p.d.f)
  • Familiarity with statistical concepts such as mean and standard deviation
  • Knowledge of integral calculus
  • Concept of statistical distributions (e.g., normal distribution)
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nokia8650
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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!
 
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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).
 
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.
 
nokia8650 said:
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)?

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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