Deriving the Gaussian density probability equation

[CuriousQuazim]

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!

 

[alan2]

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

 

[mathman]

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.

 

[CuriousQuazim]

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 ¬_¬.