Work out the variance of the gamma

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    Gamma Variance Work
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Discussion Overview

The discussion revolves around calculating the variance of the gamma function or the gamma probability distribution. Participants are exploring the properties of the gamma function, particularly in relation to its recursive nature.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant is attempting to calculate the variance of the gamma and is unsure how to determine \gamma(\alpha + 2).
  • Another participant clarifies that the property \Gamma(\alpha + 1) = \alpha \Gamma(\alpha) applies to the gamma function, suggesting that \Gamma(\alpha + 2) can be expressed as (\alpha + 1) \alpha \Gamma(\alpha).
  • There is uncertainty regarding whether the discussion pertains to the gamma probability distribution or the gamma function itself.
  • A later reply indicates a belief that the focus is likely on the gamma probability distribution.

Areas of Agreement / Disagreement

Participants have not reached a consensus on whether the topic is the gamma function or the gamma probability distribution, indicating a lack of clarity in the discussion.

Contextual Notes

There is ambiguity regarding the notation used, as one participant initially used \gamma instead of \Gamma, which may lead to confusion about the subject matter.

gerv13
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Hi, I'm trying to work out the variance of the gamma(I'm up the the part where you multiply x^2 by the function), but i don't know how to work out what

\gamma(\alpha + 2) equals to

i know I am supposed to use the fact that \gamma(\alpha + 1) = \alpha \gamma(\alpha)

but i don't understand what to do, please help
 
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It's not clear whether you are talking about the gamma probability distribution or the gamma function. The gamma function has the property that \Gamma(\alpha+1)= \alpha\Gamma(\alpha) but is normally represented by the capital \Gamma, not \gamma.

In any case, \Gamma(\alpha+ 2)= \Gamma(\alpha+1+ 1)= (\alpha+1)\Gamma(\alpha+1)= (\alpha+ 1)\alpha\Gamma(\alpha).
 


HallsofIvy said:
It's not clear whether you are talking about the gamma probability distribution or the gamma function.

gerv13 said:
Hi, I'm trying to work out the variance of the gamma

I'm not sure either, but I have to guess its the probability distribution.
 


yupp i actually meant \Gamma sorry about that. but thanks for the help
 

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