We now take a different approach to analyzing the Duke Basketball chain, Example 4.11.

0 1 2 3 0 3 2 1 0 1 0 5 5 0 2 1 0 2:5 1.5 3 6 0 0 6

(a) Find g.i / D Ei.V1/ for i D 0; 2; 3.

(b) Use the solution to

(a) to show that the number of Duke scores (visits to state 1) by time t has N1.t/=t ! 0:6896 as computed previously.

(c) Compute h.i/ D Pi .V3 < V1/ for i D 0; 2.

(d) Use this to compute the distribution of X D the number of time UNC scores between successive Duke baskets.

(e) Use the solution of

(d) to conclude that the number of UNC scores (visits to state 3) by time t has N3.t/=t ! 0:6206 as computed previously.