Student's t distribution

A standard normal divided by an independent scaled chi-squared root gives a t distribution.

Different ways to understand it

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Chi-squared distribution
A sum of squared independent standard normal variables has a chi-squared distribution.
F distribution
The ratio of independent chi-squared variables divided by their degrees of freedom has an F distribution.
Analysis of variance
ANOVA partitions variation to test mean differences under model assumptions.
Autocorrelation
Autocorrelation measures dependence between a process and its lagged values.
Bayes theorem
Bayes theorem relates conditional probabilities in opposite directions using prior probabilities and a nonzero evidence probability.