Consider a random walk in one dimension.
Consider a numberline with integers marked on it. A drunkard it at x=0 at t=0. At each time interval he jumps +1 or -1. i.e. at t=1 he can be at x=1 or x = -1
After t = n, let him be at x_n.
What is the probability that |x_n| =< a, where a is some +ve integer.
Any ideas to start on this?
Also I would later want to generalize it to include conditions like
1. x_n > a
2. x_n < b
and combine them using AND, OR.
So please advise. Thanks