Simulations

1. Simulations The basics for simulations

2. What is a Simulation? Simulation is a way to model random events, such that simulated outcomes closely match real-world outcomes. By observing simulated outcomes, researchers gain insight on the real world.

3. Why a Simulation? Some situations do not lend themselves to precise mathematical treatment. Others may be difficult, time-consuming, or expensive to analyze. In these situations, simulation may approximate real-world results; yet, require less time, effort, and/or money than other approaches.

4. The steps to creating a Simulation • 1- Describe the possible outcomes. • 2- Link each outcome to one or more random numbers. • 3- Choose a source of random numbers (random # table / calculator). • 4- Choosea random number. • 5- Based on the random number, note the "simulated" outcome. • 6- Repeat steps 4 and 5 multiple times; preferably, until the outcomes show a stable pattern. • 7- Analyze the simulated outcomes and report results.

5. The Problem: On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game. • 1- Describe the possible outcomes.

6. The Problem: On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game. 2- Link each outcome to one or more random numbers.

7. The Problem: On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game. 3- Choose a source of random numbers (random # table / calculator).

8. The Problem: On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game. • 4- Choose a random number.

9. The Problem: On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game. • 5- Based on the random number, note the "simulated“ outcome.

10. The Problem: On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game. • 6- Repeat steps 4 and 5 multiple times (lets run it 100 times) • preferably, until the outcomes show a stable pattern.

11. The Problem: On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game.

12. The Problem: On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game. • 7- Analyze the simulated outcomes and report results.

13. The Problem: You want each of the pictures of Lebron, Payton and Serena. Remember last class? When you check your wallet you find you can only afford 4 boxes of cereal. What is the probability that you will get all 3 pictures? Run the simulation at least 20 times.