The same monkey business as before: We have a sequence of i.i.d. random variables {X} with P[X = 1] = 1/2, P[X = 2] = 1/4, P[X =3] =1/4 Vi e {1, 2, 3, ...} We are interested in the pattern "1232." We want to compute the expected time for the monkey to first type "1232." a) Draw a useful picture of a Markov chain. b) Write a set of linear equations that, when solved, give the expected time we are looking for. You do not need to solve the equations. *** Note: Solving on matlab gives (E[T], ..., E[T4]) = (128, 126, 120, 96) and so the expected time is exactly 128 steps.