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Deriving the Gaussian density probability equation

  1. Feb 29, 2012 #1
    Hey ^^, new here but I already have a question haha

    Does anyone here know how the coefficient (x-μ)^2 was derived in the following equation:

    σ^3=(1/√2∏)∫(1/σ)*(x-μ)^2*exp((x-μ)^2)/(2σ^2))

    I know the general equation for density probability is (1/σ)*exp((x-μ)^2)/(2σ^2))
    but in this case I can't quite see how the coefficient came about... any help?

    Thanks in advance!
     
  2. jcsd
  3. Feb 29, 2012 #2
    Your expression looks wrong to me. Could you check it for accuracy?
     
  4. Feb 29, 2012 #3

    mathman

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    It looks like it should be σ2. The expression is essentially the definition of the variance, the second moment of the distribution centered at the mean.
     
  5. Mar 1, 2012 #4
    Oh I'm sorry that was an error on my part, it is indeed σ^2

    σ^2=(1/√2∏)∫(1/σ)*(x-μ)^2*exp((x-μ)^2)/(2σ^2))

    Ah thank you so much mathman ^^, that's what I was looking for! I'm studying engineering so sometimes they just throw mathematical equations at us with no explanation ¬_¬.
     
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