An individual traveling on the real line is trying to reach the origin. However, the larger the desired step, the greater is the variance in the result of that step.

Specifically, whenever the person is at location x, he next moves to a location having mean 0 and variance βx2. Let Xn denote the position of the individual after having taken n steps. Supposing that X0 = x0, find

(a) E[Xn];

(b) Var(Xn).