# Standard normal distribution (probability density function when μ=0 and σ^2 = 1/2)

## Description

In probability theory, the normal (or Gaussian) distribution is a very commonly occurring continuous probability distribution—a function that tells the probability that any real observation will fall between any two real limits or real numbers, as the curve approaches zero on either side. The simplest case of a normal distribution is the standard normal distribution. This is a special case (according to Gauss) where the mean of the distribution μ=0 and the variance σ2 = 1/2. A probability density function (pdf), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.

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