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Diametrically opposite vertices

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A particle performs a random walk on the vertices of a cube. At each step it remains where is with probability 1 /4, or moves to one of its neighbouring vertices each having probability 1/ 4. Let v and w be two diametrically opposite vertices. If the walk starts at v, ?nd:

(a) The mean number of steps until its ?rst return to v.

(b) The mean number of steps until its ?rst visit to w.

(c) The mean number of visits to w before its ?rst return to v.

Reference no: EM132372751

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