# Normal Distribution

A probability distribution \(N(\mu, \sigma)\) having the PDF

The parameters \(\mu\) and \(\sigma\) are equal to the mean and standard deviation respectively.

If \(\mu\) is equal to zero and \(\sigma\) is equal to one then it is known as the

\[
\phi_{\mu,\sigma}(x) = \frac{1}{\sqrt{2\pi}\sigma} e^{-\tfrac{(x-\mu)^2}{2\sigma^2}}
\]

that governs the probability of sums of random variables.The parameters \(\mu\) and \(\sigma\) are equal to the mean and standard deviation respectively.

If \(\mu\) is equal to zero and \(\sigma\) is equal to one then it is known as the

*standard*normal distribution.