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An example of strictly stationary process is one in which all X(ti)’s are mutually Independent and Identically Distributed . Such a random process is called IID random process . In this case, 15 Since the joint pdfabove does not depend on the times {ti}, the process is strictly stationary. An example of IID process is white noise (studied later)

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Literally, non iid should be the opposite of iid in either way, independent or identical. So for example, if a coin is flipped, let X is the random variable of event that result is tail, Y is the random variable of event the result is head, then X and Y are definitely dependent. They can be decided by each other.

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In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent.This property is usually abbreviated as i. i. d.. Introduction. In statistics, it is commonly assumed that observations in a sample are effectively i. i. d.

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A sequence of random variables X(1), …, X(n) that satisfies the two conditions of independence and identical distribution is called independent and identically distributed or i.i.d. Many important results in statistics, such as the central limit theorem, were formulated for i.i.d. random variables first. In some cases the assumption of i.i.d ...

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Independent implies that an element in the sequence is independent of the random variables that came before it. Identically distributed suggests that X, Y and Z have the same N ( μ, σ 2) distribution (value of parameters μ and σ for all the variables will remain the same). Consider a simpler example.

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X1,X2,...,Xnare called independent and identically distributed random variables with pdf f(x). We abbreviate independent and identically distributed as iid. Mostexperimentsinvolve n>1 repeated observationsona particular variable, thefirstobserva- tionisX1, the second isX2, and soon. EachXiisan observationon thesamevariable and eachXi

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