# Deriving the Gaussian density probability equation

1. Feb 29, 2012

### 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?

2. Feb 29, 2012

### alan2

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

3. Feb 29, 2012

### 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.

4. Mar 1, 2012

### 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 ¬_¬.