6. Let {Sn : n > 0} be a simple symmetric random walk with So = 0, and let T = min{n > 0 : Sn = 0}. Show that %3D E(min{T, 2m}) : = 2E|S2m| = 4mP(S2m = 0) for m > 0. %3D

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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6. Let {Sn : n > 0} be a simple symmetric random walk with So = 0, and let T = min{n > 0 :
Sn = 0}. Show that
%3D
E (min{T, 2m}) =
2E|S2m| = 4mP(S2m = 0)
for m > 0.
Transcribed Image Text:6. Let {Sn : n > 0} be a simple symmetric random walk with So = 0, and let T = min{n > 0 : Sn = 0}. Show that %3D E (min{T, 2m}) = 2E|S2m| = 4mP(S2m = 0) for m > 0.
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