The probability density function (PDF) of a normal distribution is given by:
\[f(x|\mu, \sigma) = \frac{1}{\sigma \sqrt{2\pi}} \exp \left( -\frac{(x - \mu)^2}{2\sigma^2} \right)\]where:
- $ \mu $ is the mean of the distribution,
- $ \sigma $ is the standard deviation,
- $ x $ is the variable
This function describes the likelihood of a random variable $ x $ falling at a particular value, based on the mean and standard deviation of the distribution.