Chernoff-type Inequality for pair-wise independent random variables
Pairwise independence is not enough for a Chernoff-type bound on the expectation.

This follows from the fact that there are $poly(n)$-size sample spaces on $n$ 0-1 random variables, where all the variables are pairwise independent, and each is variable is uniform (it is $1$ with probability $1/2$). So the expected value of their sum is $n/2$. But because there are only $poly(n)$ possible events in the sample space, even the probability that a sum is exactly a particular value $v$ is at least $1/poly(n)$ (hence, it can't be at most $1/exp(n)$).

For a reference to this sample space construction, see pages 11-12 in this survey.