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  1. I wonder how a sequence of mutually independent random variables (each with a different or same distribution) is sampled? In other words, how can a sequence of values be ensured to be samples of a sequence of independent random variables?
  2. Furthermore how is a sequence of k-wise independent random variables is sampled?

I would like to know the basic methods, and what sources for that purpose and going beyond that.

Thanks!

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are you asking for the meaning of mutually independent random variables or for a computer-based technique for generating them? if the latter, computer uniform pseudo-random generators produce a sequence of iid uniforms, from which you can derive any other sequence of independent random variables. – Xi'an Oct 27 '12 at 4:23
@Xi'an: I asked about the latter. I think your comment addressed my first part. The second part not yet. Thanks! – Tim Oct 27 '12 at 12:01
uh-oh, I though my comment answered the latter! If you use a usual random generator, your uniform variates are independent and hence anything you construct from those. Including $k$-dimensional random vectors. – Xi'an Oct 28 '12 at 11:36
The second part of my post is how to generate $n$ $k$-wise independent r.v.s, where $k \leq n$, not necessarily $n$ mutually independent r.v.s. – Tim Oct 28 '12 at 12:40

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