When standard deviation is undefined?

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Discussion Overview

The discussion centers on the conditions under which the standard deviation of a probability density function (PDF) may be undefined, particularly in the context of a specific PDF provided by a participant. The scope includes theoretical aspects of probability distributions and their properties.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the reasons for an undefined standard deviation after solving a PDF problem.
  • Another participant suggests that the issue may arise from the integral diverging when calculating variance, noting that some distributions, like the Cauchy distribution, lack finite variance.
  • A later reply provides the specific PDF, f(x) = 24/x^3, and questions the validity of this function as a density function, implying there may be missing restrictions on the variable x.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are competing views regarding the validity of the provided PDF and the conditions under which the standard deviation may be undefined.

Contextual Notes

There are limitations regarding the assumptions about the PDF, particularly concerning the range of x and the conditions necessary for it to be a valid probability density function.

socrates_1
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Hi, I just solved a probability density function problem and the standard deviation is undefined.Does anyone know why it happens?It would help to develop my understanding.Thanks.
 
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Since you provided no details about the problem or the distribution you derived, it's hard for anyone to comment. Do you mean that the integral diverges when you try to calculate the variance? That's not unusual; there are a number of distributions lacking finite variance (see: Cauchy distribution).
 
Number Nine said:
Since you provided no details about the problem or the distribution you derived, it's hard for anyone to comment. Do you mean that the integral diverges when you try to calculate the variance? That's not unusual; there are a number of distributions lacking finite variance (see: Cauchy distribution).

Thank you very much for your response.The probability density function is given by :
f(x)= 24/x^3

When I try to calculate ∫ (x^2) f(x) - (m^2) is undefined.Why this is so?
 
socrates_1 said:
Thank you very much for your response.The probability density function is given by :
f(x)= 24/x^3

That's not a valid density function. Are there any restrictions on x that you are forgetting to tell us?
 

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