p-biased product measure
= p-biased product measure
{title2=$\mu_p$}
Under the $p$-biased product measure $\mu_p$ on $\{-1,1\}^n$, the coordinates are <independent random variables> with $\mathbb P(x_i=-1)=p$ and $\mathbb P(x_i=1)=1-p$. Writing $\mu=1-2p$, $\sigma=2\sqrt{p(1-p)}$, and $\phi_i=(x_i-\mu)/\sigma$, the products $\phi_S=\prod_{i\in S}\phi_i$ form the $p$-biased <Fourier-Walsh transform>[Fourier basis].