Deriving the Gaussian density probability equation


by CuriousQuazim
Tags: density function, gaussian
CuriousQuazim
CuriousQuazim is offline
#1
Feb29-12, 08:39 AM
P: 5
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!
Phys.Org News Partner Science news on Phys.org
Scientists pinpoint when harmless bacteria became flesh-eating monsters
Asian air pollution affect Pacific Ocean storms
Rocket leak delays space station delivery launch (Update)
alan2
alan2 is offline
#2
Feb29-12, 01:17 PM
P: 188
Your expression looks wrong to me. Could you check it for accuracy?
mathman
mathman is offline
#3
Feb29-12, 04:20 PM
Sci Advisor
P: 5,935
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
CuriousQuazim is offline
#4
Mar1-12, 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)*(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 _.


Register to reply

Related Discussions
kelin gordon equation - probability density Advanced Physics Homework 0
Probability Density Function of a Quadratic Equation Set Theory, Logic, Probability, Statistics 1
Deriving Gaussian Gravity Calculus & Beyond Homework 2
[SOLVED] Klein Gordon equation, probability density Advanced Physics Homework 1
Deriving an equation for the density of air Introductory Physics Homework 0