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Concept# Gaussian function

Summary

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac{(x - b)^2}{2c^2} \right)
for arbitrary real constants a, b and non-zero c. It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell".
Gaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value μ = b and variance σ2 = c2. In this case, the Gaussian is of the form
g(x) = \frac

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