Download
1 / 20
200 likes | 308 Views
Simulations. The basics for simulations. 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.
E N D
Simulations The basics for simulations
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. How might simulations be useful in business? Science?
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.
The steps to creating a Simulation • 1- Describe the component and all the possible outcomes. • 2- Link each outcome to one or more random numbers. The probability of the outcomes must match the probability of the set of numbers matched to the outcome. • 3- Decide what a trial is and how you know when the simulation is complete? How many random numbers will simulate the trial? • 4- Determine the response variable you will be counting in the trial? How many times does your desired outcome show up? • 5- Based on the random numbers, note the "simulated“ outcome. • 6- Repeat steps 4 and 5 multiple times (20 at least); preferably, until the outcomes show a stable pattern. • 7- Analyze the simulated outcomes and report results.
The Problem: On average, suppose a baseball player hits a home run 3 in every 25 times at bat, and suppose he gets exactly three "at bats" in every game. Using a simulation, estimate the likelihood that the player will hit 2 home runs in a single game. • 1- Describe the component and all the possible outcomes. • What are the probabilities of each outcome? Pg 1.2 what is the component & outcomes M/C Pg 1.3 what are the probabilities of each outcome
The Problem: On average, suppose a baseball player hits a home run 3 in every 25 times at bat, and suppose he gets exactly three "at bats" in every game. Using a 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. The probability of the outcomes must match the probability of the set of numbers matched to the outcome. (00 represents 100) Pg 1.4 what set of 2 digit numbers will equal homeruns? other?
The Problem: On average, suppose a baseball player hits a home run 3 in every 25 times at bat, and suppose he gets exactly three "at bats" in every game. Using a simulation, estimate the likelihood that the player will hit 2 home runs in a single game. 3- Decide what a trial is or how do you know when the simulation is complete or how many random numbers will simulate the trial? Pg 1.5 what is the trial in context? Pg 1.6 M/C what is a trial in the simulation?
The Problem: On average, suppose a baseball player hits a home run 3 in every 25 times at bat, and suppose he gets exactly three "at bats" in every game. Using a simulation, estimate the likelihood that the player will hit 2 home runs in a single game. 4- Determine the response variable you will be counting in the trial? How many times does your desired outcome show up in your simulations? Each time it shows up count that as a success otherwise it is a failure. Pg 1.7 M/C what is the desired outcome or what are you going to count up?
The Problem: On average, suppose a baseball player hits a home run 3 in every 25 times at bat, and suppose he gets exactly three "at bats" in every game. Using a simulation, estimate the likelihood that the player will hit 2 home runs in a single game. 5- Run your simulation 20 times. Next page gives an example.
The Problem: On average, suppose a baseball player hits a home run 3 in every 25 times at bat, and suppose he gets exactly three "at bats" in every game. Using a simulation, estimate the likelihood that the player will hit 2 home runs in a single game. N N N N N Y N N N N 5- Run your simulation 20 times. One person start at row 2 One person at row 8 One person at row 14 And one person at row 20 Pg 1.8 list all 20 of your response variables Pg 1.9 how many successes out of 20 tries did you get?
The Problem: On average, suppose a baseball player hits a home run 3 in every 25 times at bat, and suppose he gets exactly three "at bats" in every game. Using a simulation, estimate the likelihood that the player will hit 2 home runs in a single game. • 7- Analyze the simulated outcomes and report results.
The 2nd Problem: Many married couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each sex, what would we expect the average family size to be? Assume that boys and girls are equally likely. • 1- Describe the component and all the possible outcomes. • What are the probabilities of each outcome?
The 2nd Problem: Many married couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each sex, what would we expect the average family size to be? Assume that boys and girls are equally likely. • 2- Link each outcome to one or more random numbers. The probability of the outcomes must match the probability of the set of numbers matched to the outcome. (00 represents 100)
The 2nd Problem: Many married couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each sex, what would we expect the average family size to be? Assume that boys and girls are equally likely. 3- Decide what a trial is or how do you know when the simulation is complete or how many random numbers will simulate the trial?
The 2nd Problem: Many married couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each sex, what would we expect the average family size to be? Assume that boys and girls are equally likely. 4- Determine the response variable you will be counting in the trial? How many times does your desired outcome show up in your simulations? Each time it shows up count that as a success otherwise it is a failure.
The 2nd Problem: Many married couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each sex, what would we expect the average family size to be? Assume that boys and girls are equally likely. 5- Run your simulation 20 times. see next page for example One person start at row 3 One person at row 9 One person at row 15 And one person at row 21
0-4 for a girl; 5-9 for a boy Stop when you have at least one from each set of numbers. 2 2 3 2 5 2 3 11 5 4 Find the mean and stdev of your response variable: 5+3+2+3+5+2+2+2+11+4 = 39/10 = 3.9 Stdev = 2.77
The 2nd Problem: Many married couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each sex, what would we expect the average family size to be? Assume that boys and girls are equally likely. • 7- Analyze the simulated outcomes and report results.
The 2nd Problem: Many married couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each sex, what would we expect the average family size to be? Assume that boys and girls are equally likely. • What is the likely hood that a couple will have 5 children under this scenario?
