Dirac Delta as an approximation of Normal Distribution 

Dirac Delta Function is a unique mathematical function that has a value of infinity at one point, lets say x=0 and zero everywhere else.
This function can be approximated by a normal distribution. The normal distribution which is also known as a Gaussian function, is a very common mathematical function that has applications in many physical situations. Its shape is determined by its standard deviation.
The normal distribution approximates a dirac delta function when the standard deviation approaches zero.
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