1. In honor of л day (March 14), calculate using Monte Carlo simulation in Excel. You can use the method described in the class notes. Choose a sample size n large enough to get a close approximation. 2. Consider the integral of the following function L²x10-1 a) Use the basic Monte Carlo method from the class to calculate the integral using 1,000 Unif(0,1) Ui's. Also calculate 95% confidence interval for your estimation. b) Use the second Monte Carlo method from the class (based on whether random point is below or above the curve) using 1,000 Unif(0,1) Ui's to calculate the integral. c) Calculate the error in your estimations of a and b. Then, compare two methods. Which method provides better estimate? 3. Simulate in Excel the (S,s) inventory example from class. That is, suppose that the demand is i.i.d. discrete uniform {0,1,...,, 103. Initial stock is 10 units and costs and price are given in the class notes. Simulate this system for 100 days with 2 replications for each scenario. What is the average sales revenue, average total cost and average profit for the following scenarios? What should be this store's inventory policy? Scenario 1: S-10 and s=3 Scenario 2: S-10 and s=5 Scenario 3: S-10 and s=1 Scenario 4: S-15 and s=5 4. Simulate in Excel the newspaper example from class using the template in Ninova (Newspaper_Example.xlsx). Description of the problem could be found in your textbook (Example 2.3 in BCNN). Simulate this system for 20 days if the seller decides to buy 50, 80 or 100 newspapers. Which policy is better (hint: compare the average daily profit)?