My question is..
Given one or more streams/strings/sequences composed of independent and identically distributed variables is there ANY way of combining/merging/viewing the stream/s that would create a bias or statistical dependency.
Say for example we have I.I.D events A, B, C, D, E, F. Given any finite length of sequence would we be able to simulate a statistical dependence between these events.
I am aware that by definition the events of each single outcome is independent and unbiased - so to clarify my question a little further - what I mean is - is there a way to statistically overcome the independence of outcomes by any combination of possible methods or parallel streams.
Thank you
Suppose $X_1,X_2,X_3,\ldots$ are independent identically distributed random variables. Consider the sequence $X_1+X_2, \,\,\, X_2+X_3, \,\,\, X_3+X_4, \,\,\, X_4+X_5,\,\,\,\ldots.$ Those are not independent.