1. Use the Binomial Theorem to give the expansion of: (p+q)3

2. (THIS PROBLEM COUNTS DOUBLE)
3. 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 Good Basketball 3-Point Shooters as follows: Let x be the career percentage of 3-point shots made by a player; if x > 60%, then the player is a good 3-point shooter; if x < 20%, then the player is NOT a good 3-point shooter; if 20% ≤ x ≤ 60%, 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 20% ≤ x ≤ 60%). Express your answer as a function (not an actual graph)


4. 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)

5. (THIS PROBLEM COUNTS DOUBLE)
6. Using information in the Lesson 09 Online Content and the Lesson 09 Problems of the Week, construct an Excel-compatible 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. You'll need to compute and display the probabilities for all possible outcomes of an experiment consisting of THE SUM OF ROLLING TWO DICE. Make sure to include enough labels/comments so that a user can understand what you've done. Upload your spreadsheet file to the ANGEL Drop Box along with your completed Quiz document (you'll be uploading MORE THAN ONE FILE to the Lesson 09 Drop Box, but ANGEL can handle it)

7. 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)

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:
8. 68
mWarm= 
9. 79
mWarm= 
10. 89
mWarm= 

Let x and y belong to a fuzzy set with m(x) = 0.40 and m(y) = 0.75. Calculate the membership value for:
11. NOT y
NOT y = 
12. x AND y
x AND y = 
13. x OR y
x OR y = 

14. 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", "Y", "Distance from (0, 0)", and "Point in Circle?", respectively. Check the formulas for rows 4 through 30 in columns A through D and write down the four Excel formulas from columns A through D in row 5 of the "MC Pi" worksheet

Now write down the formulas for the count of Points in Circle and Total Points (cells F8 and F11). Explain what these two formulas are calculating


Record the current value for the estimate of Pi

Now continue adding more and larger numbers of iterations three separate times, and record the new estimate of Pi for each of the three

Now try deleting iterations from the simulation three separate times and record the new estimate of Pi for each of the three


15. What would you EXPECT to happen to the estimate as you add more and more iterations?

What would you EXPECT to happen to the estimate as you remove more and more iterations?