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5975概率中等数值题medium

Expected Sample Size of a Sequential Boundary Test

题目

Independent draws X_1, X_2, ... each equal +1 with probability 0.6 and -1 with probability 0.4, accumulated into S_n. Sampling stops when S_n first reaches +5 or -5. The exit probabilities are P(exit +5)=0.883636 and P(exit -5)=0.116364. Using the linear-drift (Wald-Wolfowitz) martingale, find the expected number of draws E[N].

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