Finite Exchangeability
- a finite set {𝑦1, 𝑦2, …, 𝑦𝑛} is exchangeable if the joint probability 𝐏(𝑦1, 𝑦2, …, 𝑦𝑛) is invariant under permutations of the indices
- that is, for every permutation (𝜔1, 𝜔2, …, 𝜔𝑛) of {𝑦1, 𝑦2, …, 𝑦𝑛}; 𝐏(𝑦1, 𝑦2, …, 𝑦𝑛) = 𝐏(𝜔1, 𝜔2, …, 𝜔𝑛)
Infinite Exchangeability
- is the property that every finite subset of an infinite sequence {𝑦1, 𝑦2, …} is exchangeable