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QUESTION

# What is the Gaussian function?

The basic Gaussian function is simply:

y=e^(-x^2)

where the normal distribution is a specific parameterization:

f(x | mu, sigma^2) = 1/sqrt(2 pi sigma^2) e^(-(x-mu)^2 /(2 sigma^2))

The basic Gaussian function is simply:

y=e^(-x^2)

We can parameterize is with some additional constants:

y = A e^(-b(x-c)^2)

If we want to use it for statistical purposes, we would want to make it into where:

c becomes the mean i.e. c implies bar x b becomes the reciprocal of half of the variance, i.e. b implies 1/(2sigma^2) and we choose A such that the integral of the function over all x is 1, i.e. A implies 1/sqrt(2 pi sigma^2)

The normal distribution function is then given by

f(x | mu, sigma^2) = 1/sqrt(2 pi sigma^2) e^(-(x-mu)^2 /(2 sigma^2))