What is the Gaussian Function? Applications & Derivation

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what is gaussian function?what are it's field of applicaton?how this function is derived,i mean what are the logical reason(approach) behind forming such function?
 
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One way to motivate the gaussian distribution is to consider an outcome Y that is the result of summing many small independent contributions to the total outcome.
 

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Thread 'Detail of Diagonalization Lemma'

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