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Chapter 4

Chapter 4. Simulation. or. How to solve math problems without using “math”. Section 4.2. Introduction to Simulation. “China’s Problem” 1960. Current Policy. “One Family – Child” Incentives Reduced mortgages Preferential treatment for jobs. Penalties. No bonuses

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Chapter 4

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  1. Chapter 4 Simulation or How to solve math problems without using “math” Introduction to Simulation

  2. Section 4.2 Introduction to Simulation Introduction to Simulation

  3. “China’s Problem” 1960 Introduction to Simulation

  4. Current Policy “One Family – Child” Incentives • Reduced mortgages • Preferential treatment for jobs Introduction to Simulation

  5. Penalties • No bonuses • Financial penalties for additional children • Social stigma No promotions Introduction to Simulation

  6. Problems • No birth restrictions on foreign nationals • Urban areas vs. rural regions • Financial • Cultural Introduction to Simulation

  7. Proposed Policy “One Family – ” Examples of proposed Chinese families Introduction to Simulation

  8. Big Question . Your estimation Why is this a case for simulation? Here are some coins -You solve it Introduction to Simulation

  9. Simulation #1 - Coins Simulated Coin “Outcomes” Real Life “Outcomes” Girl Baby Boy Baby Introduction to Simulation

  10. Making Families with Coins Examples Make 10 families and report TOTAL number of kids. (Class) Average number of children per family Introduction to Simulation

  11. Repeat and pool all data Introduction to Simulation

  12. Keystrokes ON MATH (third key down, left column) Cursor over to PRB Press “5” Type: 1, 2, 1 to get RandInt(1, 2, 1) Introduction to Simulation

  13. Random Integer Correspondence Simulated Random Integer outcomes Real Life outcomes Girl Baby Boy Baby Introduction to Simulation

  14. Making Families with a TI Examples Make 10 families and report total number of children Introduction to Simulation

  15. Repeat and pool all data Introduction to Simulation

  16. Rule 1 The more trials the better your answer Introduction to Simulation

  17. In general Largest, ) RandInt ( How Many Smallest, So, RandInt(2, 8, 3) means . Examples: Introduction to Simulation

  18. 0 of 30 To get the data 2, 3, 1, 1, 3 use • RandInt(1, 5, 3) • RandInt(1, 3, 5) • RandInt(2, 5, 3) • RandInt(2, 2, 5) • None of the above Introduction to Simulation

  19. 0 of 30 Randint (3, 6, 3) could give the output • 3, 3, 3 • 4, 5, 6 • 6, 5, 6 • All of the above • None of the above Introduction to Simulation

  20. Mathematical Models • The math model in voting was a Preference schedule • The math model for simulation is RandInt(x, y, z) • What do they have in common? • Simple notions • Help solve complex problems • Wide variety of applications Introduction to Simulation

  21. Name of Problem: Chinese Population. • Outcomes whose Random integer • probabilities we know: correspondences: • RandInt( , , ) • (Trials): • Answer: Fairly complex problem is reduced to this math model. This is what we’ll seek in each problem Introduction to Simulation

  22. End of 4.2

  23. 0 of 30 If the “One Family – One Son” policy were adopted, the average number of children per family would be? (Nearest answer) • 1.5 children • 2 children • 2.5 children • 3 children • 3.5 children • More Introduction to Simulation

  24. Meta - Material

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