4. Let {Xno no be a random walk on state space {0, 1}, such that P(X1 = 0|Xo = 0) = P E (0, 1) and P(X1 = 0|Xo = 1) = r E (0, 1). (a) Show that: r r P(X100 = 0) = I-ptr t (p-r)100 P(Xo = 0) - 1 - ptr (b) If this random walk starts at 0, what is its expected number of visits to 1 before its first return to 0