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Designing Simulations: An Overview of Experimental Models and the Monte Carlo Method

This guide explores the fundamentals of designing simulations as experimental models that emulate real-life situations. Key components include defining the type of simulation method (e.g., dice, coin), determining what constitutes a single trial, and recording necessary data. The Monte Carlo Method is highlighted for its use of repeated trials to estimate specific probabilities. An illustrative example is provided, where a simulation of 100 trials is conducted to estimate the likelihood of a family with three children having exactly one boy, detailing the steps involved.

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Designing Simulations: An Overview of Experimental Models and the Monte Carlo Method

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  1. 7-7/7-8 7-7/7-8Designing Simulations

  2. 7-7/7-8 Simulations… Simulation – An experimental model of a situation that attempts to capture all aspects of the real situation that effects the outcomes. Trial – Each “running” of the simulation

  3. 7-7/7-8 Monte-Carlo Method This method uses relative frequencies obtained from repeated trials to simulate a real-life experiment and obtain specific probabilities. Steps – 1) Determine the type/kind of simulation method you will use. (Dice, coin, spinner,etc.) 2) Define what constitutes a single trial and what data will be recorded. 3) Determine the number of trials that will be run, and how the estimated answer will be obtained.

  4. 7-7/7-8 Example: You are studying the number of boys and girls with families of 3 children. Design a simulation with 100 trials to estimate the probability that a family of 3 children has exactly one boy Steps – 1) Determine the type/kind of simulation method you will use. (Dice, coin, spinner, etc.) 2) Define what constitutes a single trial and what data will be recorded. 3) Determine the number of trials that will be run, and how the estimated answer will be obtained.

  5. 7-7/7-8 Random Numbers: Grab a book and turn to page 874 (T-134)…

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