A symmetric random walk in two dimensions is defined to be a sequence of points {(X,...

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A symmetric random walk in two dimensions is defined to be a sequence of points {(X, Y): n>0} which evolves in the following way: if (X, Yn) = (x, y) then Xn+1, Yn+1 is one of the four points (x 1, y), (x, y1), each being picked with equal probability. If (Xo, Yo)=(0,0). Show that E(X22 + Y2) = n. A symmetric random walk in two dimensions is defined to be a sequence of points {(X, Y): n>0} which evolves in the following way: if (X, Yn) = (x, y) then Xn+1, Yn+1 is one of the four points (x 1, y), (x, y1), each being picked with equal probability. If (Xo, Yo)=(0,0). Show that E(X22 + Y2) = n.