First passage to ±1

What is the expected time for standard Brownian motion to first reach +1+1 or 1-1?

Show hints (2)+
  1. Use the martingale W(t)2tW(t)^2 - t and optional stopping.
  2. At TT, W(T)2=1W(T)^2=1.

Answer

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Asked at: Jane Street, Two Sigma

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