Consider one-dimensional N-step ''random walk'' problem with the
probability of making a step to the right being p and that to the
left being q ( with p + q= 1). After N steps, the walker is
somewhere between N steps to the left and N steps to the right of
the starting point, which we can coordinate as x = - N, - N +
1,...N - 1, N.
a, show that the probability with which the walker is at x = n after N steps is
p(n) =P(N+n)/2 Q(N-n)/2