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--- un:gaussian-distribution [2023/06/20 11:01] – asad
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-====== Gaussian distribution ======
-Also known as the normal distribution or bell curve, is a continuous [[probability distribution]] that is widely used in statistics, mathematics, and the natural and social sciences. It is named after the German mathematician Carl Friedrich [[Gauss]].
-The Gaussian distribution is characterized by its symmetric bell-shaped curve, which is defined by two parameters: the mean ($\mu$) and the standard deviation ($\sigma$). The mean represents the center of the distribution, while the standard deviation determines the spread or dispersion of the data.
-If a population has a normal distribution, then in a single trial the probability of getting an outcome $x$ is
-$$ P(x,\mu,\sigma) = \frac{1}{\sigma\sqrt{2\pi}} e^{[(x-\mu)/\sigma]^2/2} $$
-where $e$ is [[Euler's number]]. The distribution is shown below for three different mean and standard deviations.
-[[https://colab.research.google.com/drive/1S9shHapVuaLUiuPY84EA_mDYK6JOZVCF?usp=sharing|{{:un:gaussian.png?nolink&700|}}]]
-The full width at half-maximum $\text{FWHM} = 2.354\sigma$ and probable error $\text{PE}=0.6745\sigma=0.2865\text{ FWHM}$. The standard deviation, FWHM and PE are shown below.
-[[https://colab.research.google.com/drive/1S9shHapVuaLUiuPY84EA_mDYK6JOZVCF?usp=sharing|{{:un:normal.png?nolink&600|}}]]