Understanding exchangeability Suppose you had information of a true success rate of passing an exam from different schools, and that the 'true' success rates are similar, can you assume exchangeability is applicable to these values, or is there not enough info to assume it?,if so, then what more info is needed to make a reasonable assumption?
Also, since the values are considered similar, what would be a logical way to estimate the success rate at a say 5-th school given you have values of the true success rate from 4 schools already, is it just a simple average? I'm not sure whether the concept of exchangeability can be applied here, and generally not getting how it can be applied to similar situations, involving a sequence of numbers.    
 A: Exchangeability is a modeling concept, it cannot be applied to just "a sequence of numbers". Represent those numbers as realizations of some random variable and then we are playing. Your example is pass rate from (say) five different schools. Ask yourself: prior to seeing the actual numbers, do you expect more or less the same from the five schools? Or are there some distinguishing characteristics of some schools that make you have differing expectations? In the last case, you cannot assume exchangeability, at least not directly.
What kind of information could make you have different expectations for some schools? Some possibilities:

*

*One schools is a selective science high school, the others ordinary schools.


*some schools in rich neighborhoods, others in poor.


*Some schools private, other public.


*Most schools large, but one is small, so you expect larger variability simply from averaging over fewer students.


*...
So, exchangeability is a form of symmetry: There is symmetry in the prior information that you have. This does not at all imply independence, exchangeability is much weaker than independence. When assuming exchangeability, you can model your random variables as IID, see details here.  That should answer the question in your second paragraph. Do prediction as you would do in an IID model.
