Problem 1: One of the most widely used policies to manage inventory subject to random demand is the \"(s,S)\" policy. When the inventory level at the end of the day falls at s or below, we order enough inventory to bring it back at S. For simplicity, we assume that there is no lead time. Suppose now that an electronics store sells a video game console and uses an Inventory policy with s=2 and S =6. That Is, If the inventory level at the end of the day is either O or 1 or 2, then they order enough new units so that the total inventory level at the beginning of the next day is 6. Let Xn denote the Inventory level at the end of day n. The daily demands are independent random variables following the Binomial (4, 0.6) distribution. Today's (day 0) end-of-day inventory is 3. (a) Model the inventory level at the end of each day (day n) as a Markov Chain. Clearly define S, a(0), P. Also present the p.m.f of the demand. (20 Points) (b) Compute the expected inventory level at the end of the day 5. (5 Points) (c) Compute the probability of a stock-out during day 6. (5 Points)