(i) Let RW, = {(so.S1.. sn) : So = 0, Isi+1 – Si| = 1,i = 0, 1,...,n– 1} be the set of all possible paths of a simple random walk of length n. Show that #RW, = 2", or the number of paths in RW, is 2". (ii) Let Dn = {(So, S1,.., Sn) € RW, : Sn = 0}. Calculate the number of paths in D,?

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