Let a random walf with a certain stopping time $T$. Say that step $i$ costs $i$. If we can compute the average value of $T$, what is the correct (non biaised) way to compute the average cost?

Le $E(T)$ be the mean stopping time. Is the average cost simply $$\frac{E(T)(E(T)+1)}{2}$$ ?

Thank you.


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