11 Normal Distribution
11.2 Normal distribution
11.2.1 Definition
The normal distribution is defined by two parameters:
- \(\mu\): population mean
- \(\sigma\): population standard deviation
It is just a quirk of the normal distribution that the parameters that define it correspond to its mean and standard deviation. This will not generally be true for most other distributions that we will deal with.
11.2.2 Probability distribution
The normal distribution is continuous, and the continuous probability distributions are called probability density functions (pdfs).
The following equation defines the pdf of a normal distribution:
\[ f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{1}{2}{\frac{(x - \mu)^2}{\sigma}}} \]
