High Quality Content by WIKIPEDIA articles! In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. Any collection of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent. Pairwise independent random variables with finite variance are uncorrelated. Here is perhaps the simplest example. Suppose X and Y are two independent tosses of a fair coin, where we designate 1 for heads and 0 for tails. Let the third random variable Z be equal to 1 if one and only one of those coin tosses resulted in "heads", and 0 otherwise. Then jointly the triple (X, Y, Z) has the following probability distribution:

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