normal distribution

(NL: normale verdeling)

The normal distribution is a continuous probability distribution with two parameters: the expected value $\mu$ and the standard deviation $\sigma$.

The normal distribution with expected value $\mu = 0$ and standard deviation $\sigma = 1$ is called the standard normal distribution.

If a stochastic variable $X$ has a normal distribution with expectation value $\mu$ and standard deviation $\sigma$, then we write $X \sim \mathcal{N}(\mu, \sigma)$.

The probability density function looks like this:

$Probability density function of normal distribution for different values of $\mu$ and $\sigma$$

The cumulative probability density function (or left tail probability) looks like this:

$Probability density function of normal distribution for different values of $\mu$ and $\sigma$$