Published on *Computer Science Department at Princeton University* (http://www.cs.princeton.edu)

In this paper we develop an approach to studying probabilistic spaces

of boolean functions, namely recovering exact formulas for the event

probabilities in terms of the moments. While this involves analyzing

a large number of moments, there are situations in which this seems

feasible to do; for the $m$-fold AND of a probability space of

functions, there is a formula involving coefficients with a geometric

intepretation (and which is otherwise quite simple). We investigate

the coefficients involved in the $k$-SAT problem, where we give a

formula for the $1$-SAT coefficients and are able to understand a few

of the $2$-SAT coefficients.