A guy starts walking from position x_0 on earth (we treat earth as a sphere
with radius R). He randomly chooses a direction and walk 1 meter (this is
the spherical distance) and reaches position x_1. He repeats the walk n
times and arrives at position x_n.
Question:
(1) what is E((x_n - x_0)^2)? (here ((x_n - x_0)^2 is the square of the
Euclidean distance, not the spherical distance).
(2) does E((x_n - x_0)^2) converge when n --> \infty?
