Pardon me if the question is stupid, but I don't understand how you go about proving exchangeability of a random sequence. In the case of a distribution such as the normal distribution, I get that since it is determined by the moments, it is all about checking if the moments and covariances are "exchangeable". However, I get stumped at a different example.
Assume we have a infinite sequence of binary random variables which we know are identically distributed, but not indepedent. How do we determine if the sequence is exchangeable (in the sense given at https://en.wikipedia.org/wiki/Exchangeable_random_variables) ? If I were to guess, I would say that it is something about the covariance, but I am not sure. In practice I feel like it is not feasible to check the joint distribution...