Characteristic function in prbability

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Discussion Overview

The discussion revolves around the characteristic function in probability theory, specifically focusing on the integration techniques used to evaluate its defining integral. Participants explore the implications of their calculations and seek clarification on the results obtained.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant mentions integrating the characteristic function by parts, leading to an infinite result that seems to contradict established definitions.
  • Another participant suggests that a Taylor series expansion of the exponential function is typically used to derive moments, indicating a possible misunderstanding of the integration process.
  • Clarification is requested regarding the specific integral being evaluated, with emphasis on the definition of the characteristic function.
  • Some participants express difficulty in using LaTeX for mathematical expressions, which may hinder the clarity of their contributions.

Areas of Agreement / Disagreement

There appears to be some disagreement regarding the evaluation of the integral defining the characteristic function, with no consensus on the correctness of the initial participant's approach or the implications of their findings.

Contextual Notes

Participants have not fully resolved the assumptions underlying their calculations, and there are indications of differing interpretations of the integral's definition and evaluation methods.

Who May Find This Useful

Readers interested in probability theory, particularly those exploring characteristic functions and integration techniques in mathematical contexts.

O.J.
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I was reading about it here:
http://mathworld.wolfram.com/CharacteristicFunction.html
very neat. But then I tried out of boredom integrating the expression by parts where u = the exponential term and v = f (x) (or P(x)). The integral came out nicely as I got a term similar to the left hand side except with a different coefficient. Anyway, the evaluated integral was infinite, which contradicts with this link. Is there something wrong with my logic? Can any of you try evaluating the expression by integration by parts and show ur results? thank u
 
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I'm not sure what integral you are evaluating. From what I see a Taylor series expansion is done on the exponential function and the moments come out by definition. That said. I didn't really read the link.
 
The integral I am talking about is the integral that defines the characteristic function. the definition.
 
O.J. said:
The integral I am talking about is the integral that defines the characteristic function. the definition.

Show your steps. I think my previous comment still applies.
 
I don't know how to use that Latex math language :(...
 
O.J. said:
I don't know how to use that Latex math language :(...

You should learn, it is easy.
 

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