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Simple
Simple
2:35 AM
Let $\{S_n\,:\,n\geq0\}$ be a simple random walk with $p$ be the probability of stepping up and $q=1-p$ be the probability of stepping down. Let $T_k=\min\{n\geq1\,;\,S_n=k\}$. If $p<1/2$, is $E(T_1\,|\,T_1<\infty)<\infty$?
So far, I have the generating function $G(s)=\frac{1-\sqrt{1-4pqs^2}}{2qs}$
I know that $E(T_1)=\infty$ when $p<1/2$
 

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