Please help me with this question. It is simple, but I am confused right now.
For $i=1,...,n$, $\alpha_i \in C$ and $r_i$ independent and is such that $P(r_i=1)=1-P(r_i=-1)$.
I know that $E|\sum_{i=1}^n\alpha_i r_i|^p\leq C \sqrt p \| \alpha \|_2$.
I need to bound $E|\sum_{i=1}^{n-1}(\alpha_i-1) r_i|^p$.
Thank you