> For the complete documentation index, see [llms.txt](https://wiki.ainzzorl.lol/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://wiki.ainzzorl.lol/math-1/probabilities-and-statistics.md).

# Probabilities & Statistics

## Probability vs Likelihood

Probabilities attach to results; likelihoods attach to hypotheses.

E.g. probability of certain result given distribution; likelihood that the distribution is this given an observed result.

We usually consider ratios of likelihoods to compare hypotheses.