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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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Question

A symmetric random walk in two dimensions is defined to be a sequence of points {(Xn, Yn):
n≥ 0} which evolves in the following way: if (Xn, Yn) = (x, y) then (Xn+1, Yn+1) is one of the
four points (x ±1, y), (x, y ± 1), each being picked with equal probability. If (Xo, Yo) = (0,0):
(a) show that E(X2 + Y2²) = n,
(b) find the probability po (2n) that the particle is at the origin after the (2n)th step, and deduce that
the probability of ever returning to the origin is 1.

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