← 返回数学题库
525概率中等数值题medium

Expected Ruin Time via Martingale Method

题目

A biased random walk on {0,1,,10}\{0, 1, \ldots, 10\} with absorbing barriers at 00 and 1010 moves +1+1 with probability p=0.6p = 0.6 and 1-1 with probability q=0.4q = 0.4. Starting from state 33, use the martingale Mn=XnμnM_n = X_n - \mu n (where μ=pq\mu = p - q) and the optional stopping theorem to find the expected absorption time E[τ]E[\tau].

解题计时

0:00

提交作答时记录,用于后续平均用时统计。

你的答案