Independent Identically Distributed. A sequence of random variables X1, X2, ... is said to be IID if the Xi are all independent variables, but X1 has the same distribution as Xi for all i.

This is the standard setting for most of the common problems of probability: a sequence of coin tosses, arrival times in a queuing model, and the coordinates of a point chosen in an n-dimensional cube according to the uniform distribution are all examples of IID sequences.

But not everything is IID. For instance, in a Markov chain the variables generally are not independent, so even if we start the chain from a stationary distribution we don't get an IID sequence. And the coordinates of a point chosen uniformly at random inside the box [0,1]×[0,2]×[0,3]×[0,4] are independent, but each follows a different distribution, so they're not IID either.

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