Let $x$ be vector in $R^n$. Let $\pi(⋅)$ be a permutation on the set $\{1,\ldots,n\}$ with a uniform distribution. Let $|m|\leq n, m \in Z$.
Using Bernoulli (or maybe some other) distribution approimate the $q$-th moment $$ E\left|\sum_{i=1}^mx_{\pi(i)}\right|^q, \quad q\geq 2. $$
Thank you.