In Problem 123, let E[T] denote the expected time until the particle reaches 1

(a) Show that 1/(2p-1) if p > 1/2 E[T] = 00 if p 1/2

(b) Show that, for p > 1/2, 4p(1-p) Var(T) = (2p-1)

(c) Find the expected time until the particle reaches n, n > 0.

(d) Find the variance of the time at which the particle reaches n, n > 0