Distribution - Normal

The most famous of the distributions. We associate it with Linear regression because we assume that the error term is normally distributed.

Mathematics

Note, the multiplier ($\frac{1}{\sqrt{2\pi {\sigma }^2}}$) is to normalize the Probability Density Function to equal 1.

How does it relate to other distributions?

1. With the Distribution - Gamma, as you increase the shape parameter, the Gamma distribution approaches normal (important for simulating wait times)
2. It can be an approximation to a Distribution - Binomial
3. Distribution - Beta

Code

R

### Generating normal distributions
rnorm()

Python

References

1. https://math.stackexchange.com/questions/384893/how-was-the-normal-distribution-derived#:~:text=The key to derive the,i.e. to choose X1