$U_n$ be an iid binary random process with $P_r\{ U_{n}=1\}=P_r\{U_n=-1\}=0.5 , \forall n$. what is the expected value of the $U_0$?
I think $U_0$ may be the first time in this binary random process,but i am not sure that the $E[ U_0]$ will be $0.5$ just because the probability of $1$ and $-1$ are both $0.5$.