We consider approximations of probability disrtibutions over Z_(p)~(n). We present an approach to estimate the quality of approximations toward the construction of small probability spaces which are used to derandomize algorithms. In contrast ot results by Even et al. [13], our methods are simple, and for reasonably small p, we get smaller sample spaces. Our considerations are motivated by a problem which was mentioned in recent work of Azar et al. [5], namely, how to construct in time polynomial in n a good approximation to the joint probability distribution of i.i.d. random variables X_1...,X_n where each X_i has values in {0,1}. Our considerations improve on results in [5].
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