If you open up a classical statistics book, you will see endless amounts of information about hypothesis testing, confidence intervals, p-values, etc. Although those topics are important, I have noticed that some people walk away not having a deep understanding of probability distributions (beyond the normal distribution of course). Here are four probability distributions every statistics students should know:

Gaussian distribution

Example of munin graphs

The Gaussian distribution, also known as the normal distribution. It describes the distribution of sum of independent, identically distributed random variables.



The T is said to be normally distributed. The average of this sample:

Is also normally distributed, and this is actually more important because the Gaussian distribution describes the distribution of average.

Chi-Squared distribution


The Chi Squared distribution describes the distribution of squared sums of independent, identically distributed random variables.



The T will follow a chi-squared distribution. The reason this is important because the variance is a sum of squares, hence the chi-squared distribution is used to describe the distribution of variances.

The T-distribution


The student t-distribution describes the ratio of a Gauassian random variable with a Chi-Squared random variable. A t-distribution is basically a Gaussain distribution with fatter tails.

Fisher’s F distribution

The F-distribution describes the distribution of the ratio of two chi-squared variables. The is useful if you want to compare two variances against eachother.[1] It is used heavily in Analysis of Variance (ANVOA).

[1] Data Analysis with Open Source Tools