Let $X_1,X_2,X_3,\cdots$ variables i.i.d., such that $P(X_1=2)=1/2=P(X_1=-1)$ Let $S_n=X_1+\cdot+X_n$ consider stopping time $\tau=\{n\geq 1:S_n=10, \ or\ S_n=-10\}$. If $E(\tau )=8$. Compute $P(S_\tau = 10)$.
How can I approach this problem, as start?