(b) if at the end of week 1 there were five items in inventory, what is the probability that there will be five items in inventory at the end of week 2? (c) If at the end of week 1 there were five items in inventory, what is the probability that there will be five items in inventory at the end of week 3? (d) Over the long run, what fraction of time will the inventory be 0 at the end of the week? (e) If the inventory currently is 3, what is the expected number of consecutive weeks that it will remain at that level? as the Markov matrix for X is as follows. (0.15 0.10 0.40 0.20 0.10 0.05 0.15 0.10 0.40 0.20 0.10 0.05 0.10 0.40 0.20 0.10 0.05 0.15 P= 0.65 0.20 0.10 0.05 0.00 0.00 0.25 0.40 0.20 0.10 0.05 0.00 0.15 0.10 0.40 0.20 0.10 0.05 (b) if at the end of week 1 there were five items in inventory, what is the probability that there will be five items in inventory at the end of week 2? (c) If at the end of week 1 there were five items in inventory, what is the probability that there will be five items in inventory at the end of week 3? (d) Over the long run, what fraction of time will the inventory be 0 at the end of the week? (e) If the inventory currently is 3, what is the expected number of consecutive weeks that it will remain at that level? as the Markov matrix for X is as follows. (0.15 0.10 0.40 0.20 0.10 0.05 0.15 0.10 0.40 0.20 0.10 0.05 0.10 0.40 0.20 0.10 0.05 0.15 P= 0.65 0.20 0.10 0.05 0.00 0.00 0.25 0.40 0.20 0.10 0.05 0.00 0.15 0.10 0.40 0.20 0.10 0.05