Variable distribution equivalence

An Equivalence relation $(\sim)$ may be defined on random variables that share the same distribution, such that

𝑋 \sim 𝑌 ⟺ \forall 𝑡 \in ℝ 𝐹 𝑋 (𝑡) = 𝐹 𝑌 (𝑡)

It is immediately clear that this forms an equivalence relation. This is useful since it allows the modelling of one random variable using another one. Particularly, it is common to compare a random variable to archetypal distributions in this way, e.g. $𝑋 \sim B i n (𝑛, 𝑝)$ .

#state/tidy | #SemBr