Independent and Identically Distributed
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In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d.) if each random variable has the same probability distribution as the others and all are mutually independence (probability theory)|independent. The abbreviation i.i.d. is particularly common in statistics (often as iid, sometimes written IID), where observations in a statistical sample|sample are often assumed to be effectively i.i.d. for the purposes of statistical inference. The assumption (or requirement) that observations be i.i.d. tends to simplify the underlying mathematics of many statistical methods (see mathematical statistics and statistical theory). However, in practical applications of statistical modeling the assumption may or may not be realistic. The generalization of exchangeable random variables is often sufficient and more easily met. The assumption is important in the classical form of the central limit theorem, which states...
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