Question: Let { X n } be a symmetric simple random walk starting from 0, in each step, the value of the process will increase or

Let {Xn } be a symmetric simple random walk starting from 0, in each step, the value of the process will increase or decrease by 1 with equal probability p = 1/2, independent from other steps, and X0=0 . Let Ti = min{n > 0 : Xn = i} be the first visit time to state i.

i) What is P(T2 < | X0=0 )

ii) Show E(T2 | X0=0 )=

iii) What is E(min{T2 , T2 })

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