2. Suppose there are 2 items in stock at the beginning of the day. Assume that the inventory will not be replenished during the day and that there are no backorders. Suppose the demand D during the day has p.m.f. PD(k) = Je(4-k), for k=0,1,2,3; otherwise. (a) Determine the value of c. (b) What is the probability that the initial inventory is sufficient to cover the demand for the day? (Also, express what you are to compute symbolically rather than in words.) (c) Compute the mean demand. (Also, express what you are to compute symbolically rather than in words.) (d) Give an expression for the number of items sold during the day as a function of the demand. (Also, express what you are to compute symbolically rather than in words.) (e) Compute the expected number of items sold during the day via LOTUS. (Also, express what you are to compute symbolically rather than in words.) (f) Give an expression for the sales lost due to insufficient inventory as a function of the demand. (Also, express what you are to compute symbolically rather than in words.) (g) Compute the expected number of lost sales during the day via LOTUS. (Also, express what you are to compute symbolically rather than in words.)