1. MAT 4830 Mathematical Modeling Section 1.4 Conditional Statements http://myhome.spu.edu/lauw

2. Preview Review Binomial Distribution Introduce the first type of repetition statements – the for loop Allow a specific section of code to be executed a number of times Introduces simple arrays

3. Example 0

9. Binomial Distribution B(n,p)

11. Team HW #1

12. Team Homework #1 Use the definition of expected value and the binomial theorem Do not use the moment generating function. You may need to recall how to shift indices in a summation (see the hidden slides below for review).

13. Index Shifting Sigma representation of a summation is not unique

14. Index Shifting Sigma representation of a summation is not unique

15. Index Shifting Sigma representation of a summation is not unique

16. Index Shifting Sigma representation of a summation is not unique

17. Index Shifting Rules

18. decrease the index by 1 increase the i in the summation by 1

19. Index Shifting Rules increase the index by 1 decrease the i in the summation by 1

20. Example

21. Team Homework #2 A campaign staff knows from experience that only one in every three volunteers called will actually show up to distribute leaflets.

22. Team Homework #2 How many phone calls must be made to guarantee at least 20 workers with a confidence of 90%?

23. Team Homework #2 How many phone calls must be made to guarantee at least 20 workers with a confidence of 90%? Minimum

24. Team Homework #2 Use a binomial model to solve the problem. You need to write a Maple program to help you solve the problem. You need to explain your methodologies, arguments, and conclusions carefully. Extra works are welcome – In the past, students had done more than they were asked to get bonus points.

25. Zeng Section 1.4 Introduce the first type of repetition statements – the for loop Allow a specific section of code to be executed/repeated a number of times Introduces simple arrays

26. Zeng Section 1.4 Please listen to the explanations before you type in the program. It takes one minute to explain.

27. Example 1 Print the square of the first 10 positive integers What is the task being repeated?

28. Example 1

29. 1210 14100

30. Example 1 > sq(); 1 4 9

31. Structure of the for loop

32. The loop_index increase by the default step size 1 everytime the execution of block of statements to be repeated is finished. Different step size can be used by adding “ by stepsize ” feature.

33. Example 2 Print the square of the first 10 positive odd integers

34. Example 2

35. > sq2(); 1 9 25

36. Example 3

40. > sq3(2); 1, 4 > sq3(5); 1, 4, 9, 16, 25

41. Example 4 Fibonacci sequence is defined by

42. Example 4

43. Why there is no print statement?

44. Example 4

45. Example 5

46. This is to demonstrate the basic form of “accumulation”.

47. Example 5

50. Homework See course webpage Read 1.3 All HW due next Monday Attempt your HW ASAP Individual HW**