Compute expected coin flips to meet on octagon

Q: Compute expected coin flips to meet on octagon

This question evaluates proficiency in stochastic processes, discrete-time random walks, Markov chain hitting times, and expected value computation within probabilistic modeling.

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Question

Meeting Time on a Random Walk Around an Octagon

Problem

Two independent particles start at opposite vertices (four edges apart) of a regular octagon. At each discrete time step, each particle flips a fair coin: heads moves one step clockwise; tails moves one step counterclockwise. Two coins are flipped per time step (one for each particle).

What is the expected total number of coin flips required until the two particles occupy the same vertex?

Compute expected coin flips to meet on octagon

Meeting Time on a Random Walk Around an Octagon

Problem

Solution

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Compute expected coin flips to meet on octagon

Overview

Meeting Time on a Random Walk Around an Octagon

Problem

Solution

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