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Deriving the Gaussian density probability equation 
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#1
Feb2912, 08:39 AM

P: 5

Hey ^^, new here but I already have a question haha
Does anyone here know how the coefficient (xμ)^2 was derived in the following equation: σ^3=(1/√2∏)∫(1/σ)*(xμ)^2*exp((xμ)^2)/(2σ^2)) I know the general equation for density probability is (1/σ)*exp((xμ)^2)/(2σ^2)) but in this case I can't quite see how the coefficient came about... any help? Thanks in advance! 


#2
Feb2912, 01:17 PM

P: 206

Your expression looks wrong to me. Could you check it for accuracy?



#3
Feb2912, 04:20 PM

Sci Advisor
P: 6,102

It looks like it should be σ^{2}. The expression is essentially the definition of the variance, the second moment of the distribution centered at the mean.



#4
Mar112, 04:46 AM

P: 5

Deriving the Gaussian density probability equation
Oh I'm sorry that was an error on my part, it is indeed σ^2
σ^2=(1/√2∏)∫(1/σ)*(xμ)^2*exp((xμ)^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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