Estimation of expected value of function of i.i.d. Bernoulli random variables

March T. Boedihardjo

Published 2019-09-12Version 1

We estimate the expected value of certain function $f:\{-1,1\}^{n}\to\mathbb{R}$. For example, with computer assistance, we show that if $A$ is the adjacency matrix of $(\mathbb{Z}/15\mathbb{Z})\times(\mathbb{Z}/15\mathbb{Z})$ and $D$ is a diagonal $225\times 225$ matrix with independent entries uniformly distributed on $\{-1,1\}$, then the expected value of the normalized trace of $(6I-(D+A))^{-1}$ is between $0.2006$ and $0.2030$.