The Normal Distribution ======================= > Output automatically refreshes 5 seconds after editing markdown! The normal (or Gaussian) distribution is defined as follows: $$latex f(x;\mu,\sigma^2) = \frac{1}{\sigma\sqrt{2\pi}} e^{ -\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2 } $$ To generate random draws from a normal distribution we use the **rnorm** function: ```{r block1} output <- rnorm(1000, 100, 15); ``` The normal distribution has the typical bell shape: ```{r block2, fig.width=8, fig.height=5} library(ggplot2) qplot(output) ``` ## Kernel density estimation We can perform density estimation on the sample: ```{r block3, fig.width=8, fig.height=5} plot(density(output)) ``` ## Carl Friedrich Gauß This little guy had something to do with it !['Gauss'](