Section 55 Normal Distribution: PDF

55.1 Probability Density Function

• The Normal distribution is characterized by two parameters:

  • the mean, \(\mu\)

  • the variance, \(\sigma^2\)

• We can write: \[ \large X \sim N(\large\mu, \sigma^2) \]

• If the random variable \(X\) follows Normal distribution with parameters \(-\infty < \mu < +\infty\) and \(\sigma > 0\), then the probability density function of \(X\) is:

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