| Independent Identically-distributed Random Variables |
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Information AboutIndependent Identically-distributed Random Variables |
| CATEGORIES ABOUT INDEPENDENT AND IDENTICALLY-DISTRIBUTED RANDOM VARIABLES | |
| probability theory | |
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In Probability Theory , a Sequence or other collection of Random Variable s is independent and identically distributed (i.i.d.) if each has the same Probability Distribution as the others and all are mutually Independent . The Abbreviation ''i.i.d.'' is particularly common in Statistics (sometimes written ''IID''), where observations in a Sample are often assumed to be (more-or-less) 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. But in practical applications this may or may not be realistic. This is important in the classical form of the Central Limit Theorem , the sum of i.i.d. variables with finite Variance approaches a Normal Distribution . EXAMPLES The following are examples or applications of independent and identically distributed (i.i.d.) random variables:
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