Using the ballot theorem, show that for a SSRW starting from 0,

P(S1"0,,,,,,,Sn is greater than 0) = ES+n/n

Where S+n= max (Sn,0)

Consider a simple symmetric random walk starting from 0 and let Ta be the first

time that state a will be visited. Derive the formul for P(Ta < ) in detail.

Consider a simple symmetric random walk starting from 0 and let Ta be the first

time that state a will be visited. Find a formula for P(Ta = n), n Z.