Let $f_i, i=1, \ldots, n$ be independent Steinhaus random variables, i.e. variables which are uniformly distributed on the complex unit circle. Let $a \in R^n$.
1) Find $E\left(\sum_{i=1}^nf_i a_i\right)^{-k}$, for $k=1,2$
2) What would mean the following condition: $\|f\|_{\infty}> b \|f\|_2$, where $b<1$ and $\|f\|_{\infty}$ is the maximum part of the real parts of $f_i$