(Probability:)

**I**ndependent **I**dentically **D**istributed. A sequence of random variables `X`_{1}, `X`_{2}, ... is said to be IID if the `X`_{i} are all independent variables, but `X`_{1} has the same distribution as `X`_{i} 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.