What is the expected value of the distance you travel
You are randomly placed in the interior of a circle of radius 1 (uniform distribution). You randomly choose a direction (uniformly) and begin to walk that way, stopping when you get to the circle. What is the expected value of the distance you travel? $8/{3\pi}$ 首先各个方向是均匀的,不妨指定最后总是朝一个方向走,结果平均距离是相同的。不妨只计算向x轴正方向走的平均距离。同样,总向正方形走和总向负方向走的平均距离也是相同的。对于园内任意一个点,上诉俩方法的总距离总是过这点水平方向上弦长。
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