  We estimate the expected value of certain function
$f:\{-1,1\}^{n}\to\mathbb{R}$. For example, with computer assistance, we show
that if $\Delta$ is the Laplacian of the Cayley graph of
$(\mathbb{Z}/15\mathbb{Z})\times(\mathbb{Z}/15\mathbb{Z})$ and $D$ is a
diagonal $225\times 225$ matrix with entries chosen independently and uniformly
from $\{-1,1\}$, then the expected value of the normalized trace of
$(2I+D-\Delta)^{-1}$ is between $0.2006$ and $0.2030$.
