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5963概率简单数值题medium

Wald's Identity from Optional Stopping

题目

Let X_1,X_2,... be i.i.d. with mean 4, and let N be a stopping time (with respect to the X's) with E[N]=10. Using the martingale M_n = sum_{i<=n} X_i - 4n and optional stopping, find E[X_1+...+X_N].

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