What are the expected value and the standard deviation of the net profit made by the pharmacist on this medicine in any given month?
At the beginning of every month, a pharmacist orders an amount of a certain costly medicine that comes in strips of individually packed tablets. The wholesale price per strip is $100, and the retail price per strip is $400. The medicine has a limited shelf life. Strips not purchased by month’s end will have reached their expiration date and must be discarded. When it so happens that demand for the item exceeds the pharmacist’s supply, he may place an emergency order for $350 per strip. The monthly demand for this medicine takes on the possible values 3, 4, 5, 6, 7, 8, 9, and 10 with respective probabilities 0.3, 0.1, 0.2, 0.2, 0.05, 0.05, 0.05, and 0.05. The pharmacist decides to order eight strips at the start of each month. What are the expected value and the standard deviation of the net profit made by the pharmacist on this medicine in any given month?