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In many practical problems, samples are not independent, so the concept of dependent random variables in probability and statistics is mentioned. Exchangeable random variables is a major type of dependent random variable. As the fundamental structure theorem of infinite exchangeable random variables sequences, the De finetti’s theorem states that infinite exchangeable random variables sequences is independent and identically distributed with the condition of the tail σ-algebra. So some results about independent identically distributed random variables is similar to exchangeable random variables. By using reverse martingale approach, some scholars have given some results. In this paper we do some researches about the similarity and difference of identically distributed random variables and exchangeable random variables sequences, mainly discuss the limit theory of exchangeable random variables.
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Author(s): Huang Zhaoxia
Identically distributed random variables, dependent random variables, exchangeable random variables