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Independent and Identically Distributed

Independent and identically distributed random variables X_1, ..., X_n are mutually independent and have a common distribution function. Independence and identical distribution are separate requirements, and neither one implies the other.

Independent and identically distributed observations are often abbreviated i.i.d. This assumption permits many sampling distributions and asymptotic results to depend on a single common population distribution.

See also

Distribution Function, Independent Statistics, Random Variable, Sample

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References

Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, 1984.

Cite this as:

Weisstein, Eric W. "Independent and Identically Distributed." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IndependentandIdenticallyDistributed.html

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