Can you please answer Problem 3 and provide a detailed answer/explanation (Subject: Stochastic Operations Research)

Please submit your work via Blackboard: 1. A single pdf file includes the following: a. Main results and discussions b. For part (a) of problems 1 4, please list all the simulation output using CFRN 2. An excel file contains your simulations Definition: Chen's Favorite Random Numbers (CFRN) : {0.025,0.075,0.125,0.175,, 0.875,0.925,0.975}. There are 20 numbers in this set. Obviously, these are not good random numbers. However, we will use these numbers several times in our assignments. For your convenience, there is an Excel file containing CFRN available at Blackboard. 3. We are considering investing money on four stocks which look equally promising. Let Xi be the price (in dollars) of stock i one year from now. X1 is N(25,102),X2 is N(25,102),X3 is N(25, 102), and X4 is N(25,102). So these four stocks have the same statistical distribution. Assume that X1,X2,X3, and X4 are independent random variables. (i) If I buy one share of each of the four stocks, find the mean and variance of the "total value" of my stocks one year from now. (ii) What is the probability that one year from now my total stock value is higher than $120 ? Like Problems 1 and 2, please answer the above 2 sub-questions using CFRN and rand(): (a) (10 points) Use CFRN to generate 5 sets of random numbers for X1,X2,X3, and X4, and conduct 5 simulation runs. Specifically, use the first 4 four CFRN to generate X1, X2,X3, and X4 in simulation 1, next four 4 CFRN for the second simulation, etc. In total, you can do 5 simulation runs using CFRN. (b) (5 points) Use the function rand() in Excel to generate X1,X2,X3, and X4. And increase the number of simulation runs from 5 to 200