Gaussian Function: Definition & Relation to Gaussian Distribution

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The Gaussian function is a mathematical function characterized by its bell-shaped curve, defined by the equation f(x) = a * exp(-((x-b)^2)/(2*c^2)), where 'a' is the height, 'b' is the center, and 'c' controls the width. It is closely related to the Gaussian distribution, which describes how values are distributed around a mean in statistics, often referred to as the normal distribution. The properties of the Gaussian function, such as symmetry and the area under the curve, are integral to understanding statistical concepts. The discussion references an article that provides a comprehensive overview of the Gaussian function and its applications. Understanding these concepts is essential for fields such as statistics, physics, and engineering.
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what is gaussian function?how this is related to gaussian distribution?
 
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Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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