等间隔公交等待时间

Bus Wait I

专题: Probability / 概率
难度: L2
来源: QuantQuestion

题目详情

公交车每 10 分钟一班。你在一天中随机时刻到站（均匀随机）。问：到下一班车到来的期望等待时间是多少（分钟）？

You are anticipating the arrival of a bus to reach an interview on time! The bus operates on a consistent schedule, arriving every $10$ minutes. If you show up at a randomly chosen time during the day, what is the expected duration until the next bus arrives (in minutes)?

解析

等待时间在 $[0,10]$ 上均匀分布，期望为 $10/2=5$ 分钟。

Original Explanation

Since you arrive at a uniformly random moment during the day, the wait time until the next bus is uniformly distributed between $0$ and $10$ minutes. Thus, the expected value is simply $5$ , which represents the average of this random variable.