Question: Prove the following statement: A simple random walk will return to the origin if and only if p = 1/2. Further, when p = 1/2,

Prove the following statement: A simple random walk will return to the origin if and only if p = 1/2. Further, when p = 1/2, the time T to first return to the origin has pgf 1 (1 z² )^1/2 , and

E(T) = .

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