Suppose the demand during a lead time D is a random variable with probability mass function PD(x)= = { for x = 10, 20, 30, 40, 50 0 otherwise (a) Determine the expected demand E[D]. (b) Determine the variance of the demand . For the following, assume that the on-hand inventory is 30 units and then the random demand above is incurred. The surplus is the amount of positive OHI remaining, e.g., if the demand is 10, the surplus will be 20; if the demand is 50, the surplus will be 0. Assume that unmet demand is backlogged. The shortage is the amount of backlogged demand, e.g., if the demand is 10, the shortage will be 0; if the demand is 50, the shortage will be 20. (c) Determine E[surplus] after the demand occurs. (d) Determine E[shortage] after the demand occurs.