Download independent identically distributed

independent identically distributed∗
CWoo†
2013-03-21 17:36:10
Two random variables X and Y are said to be identically distributed if
they are defined on the same probability space (Ω, F, P ), and the distribution
function FX of X and the distribution function FY of Y are the same: FX = FY .
d
When X and Y are identically distributed, we write X = Y .
A set of random variables Xi , i in some index set I, is identically distributed
d
if Xi = Xj for every pair i, j ∈ I.
A collection of random variables Xi (i ∈ I) is said to be independent identically distributed, if the Xi ’s are identically distributed, and mutually independent (every finite subfamily of Xi is independent). This is often abbreviated as
iid.
For example, the interarrival times Ti of a Poisson process of rate λ are
independent and each have an exponential distribution with mean 1/λ, so the
Ti are independent identically distributed random variables.
Many other examples are found in statistics, where individual data points
are often assumed to realizations of iid random variables.
∗ hIndependentIdenticallyDistributedi created: h2013-03-21i by: hCWooi version: h35977i
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