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随机游走停在 0 或 3

Consider a random walk

专题
Probability / 概率
难度
L4

题目详情

Consider a random walk starting at 1 and with equal probability of moving to the left or to the right by one unit, and stopping either at 0 or at 3.

(i) What is the expected number of steps to do so?

(ii) What is the probability of the random walk ending at 3 rather than at 0 ?

解析

与上一题相同。

E[步数]=2,P(终止于 3)=13.\boxed{\mathbb{E}[\text{步数}]=2},\qquad \boxed{\mathbb{P}(\text{终止于 }3)=\frac13}.