IST 230 Lesson 9 Binomial Theorem, Fuzzy Sets, Monte Carlo Simulation 1. Use the Binomial Theorem to give the expansion of: (p+q)3 2. Using information in the Lesson 09 Online Content and the Lesson 09 Problems of the Week, create a membership function m(x) for the fuzzy set of Experienced Project Managers as follows: Let x be the number of years of PM experience; if x < 2.0, then m(x) = 0.0; if x > 8.0, then m(x) = 1.0; if 2.0 x 8.0, then m(x) should be a linear function in the range 0.0 to 1.0 (i.e., when graphed, m(x) should be a sloped line for 2.0 x 8.0). Express your answer as a function (not an actual graph) 3. Research an application of Fuzzy Sets/Fuzzy Logic. Write a brief paragraph describing the application (what is the problem it addresses; why was a Fuzzy System chosen as a solution; pros and cons of the Fuzzy solution; etc.). To get credit for this question you may NOT rely solely on the online Course Content as your only source of information (and you must properly cite your sources) 4. Using information in the Lesson 09 Online Content and the Lesson 09 Problems of the Week, describe in detail how you would construct an Excel worksheet for a Monte Carlo simulation of rolling a pair of dice. HINT: The Excel function RANDBETWEEN(x, y) generates a pseudorandom number between x and y. Make sure to give enough detail that an IST major could build such a worksheet by following your directions 5. Research an application of Monte Carlo (MC) Methods. Write a brief paragraph describing the application (what is the problem it addresses; why was Monte Carlo chosen as a solution; pros and cons of MC; etc.). To get credit for this question you may NOT rely solely on the online Course Content as your only source of information (and you must properly cite your sources) 6. Using the fuzzy membership functions from Tables 7 and 8 in the Online Course Content, calculate the applicable degree of membership using the MWarm() membership function for the following temperatures: a. 68 mWarm= b. 79 mWarm= c. 89 mWarm= Larry Newcomer WorkfileContents.doc Page 1 of 3 The Course Content and textbook are the ONLY sources of help that may be used for this exam IST 230 Lesson 9 Binomial Theorem, Fuzzy Sets, Monte Carlo Simulation 7. Let x and y belong to a fuzzy set with m(x) = 0.40 and m(y) = 0.75. Calculate the membership value for: a. NOT x NOT x = b. x AND y x AND y = c. x OR y x OR y = 8. Download and open the Excel workbook file named \"Monte Carlo Calculation of Pi.xlsx\" from the Lesson 9 folder, and make sure the worksheet named \"MC Pi\" is selected. The worksheet should contain 27 rows (4 through 30) with formulas; the column headings should be \"X\