# How does one actually determine if a sequence is exchangeable

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...

• Usually, this is not "determined" but is assumed. There is no mathematical way to resolve your question unless additional information is supplied about that infinite sequence of variables. – whuber Apr 27 '20 at 13:07
• I mean, that is kind of my question. What information about the ffds needs to be supplied to be able to make that conclusion? – edo Apr 27 '20 at 13:08
• What are the "ffds"? – whuber Apr 27 '20 at 13:15
• stats.stackexchange.com/questions/344794/… – kjetil b halvorsen Oct 6 '20 at 17:48