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Problem #103 MEDIUM

The Drunkard's Walk Home

Paradox Probability Math

Problem Statement

A man stumbles out of a bar and takes random steps — each step equally likely to go left or right by 1 metre. After n steps, how far from the bar is he on average? More precisely, what is his expected distance (root mean square distance) from the starting point? Now suppose he takes steps in 2D — equally likely to go North, South, East, or West. What is his expected distance after n steps? What about 3D?

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