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Monte Carlo Simulation. Presented by Megan Aldrich and Tiffany Timm. What is Monte Carlo?. Uses random numbers to generate a simulation to mimic real data Helps find statistics for data that is really messy Use of a computer is required. Discovery and First Use.

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Monte Carlo Simulation

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Monte carlo simulation l.jpg

Monte Carlo Simulation

Presented by Megan Aldrich and Tiffany Timm


What is monte carlo l.jpg

What is Monte Carlo?

  • Uses random numbers to generate a simulation to mimic real data

  • Helps find statistics for data that is really messy

  • Use of a computer is required


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Discovery and First Use

  • First used by Enrico Fermi in 1930s for neutron diffusion

  • Documented by John von Neumann in the 1940’s during the Manhattan Project of World War II

  • Popular because gambling was a rising sport and was coined the name Monte Carlo by Neumann’s partner Stainslaw Ulam who loved poker


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Pros

  • Easy to use

  • Can make the complex data simple

  • Does not take a lot of time to analyze

  • Inexpensive


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Cons

  • Original expense to develop and operate simulations can be high

  • Not sufficient in dealing with small numbers and usually has the operator estimating when this happens


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Outline for Monte Carlo

  • List all possible outcomes for each event.

  • Determine the probability of each outcome.

  • Determine subsets of the integers which have the same relative frequencies as the probabilities.

  • Set up a correspondence between the outcomes and the subsets.

  • Select a random number.

  • Using each random number to represent the corresponding event, perform the experiment and note the outcome.

  • Repeat until desired confidence.


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Our Problem

As the owner of a small grocery store you have a choice of hiring:

  • Two cashiers who do their own bagging, and each of whom can check out a shopper in two minutes, or

  • One cashier and one bagboy who, working as a team, can check out a shopper in one minute.

    We want to find the best scenario.


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Our Problem continued

Based on our experience for every one minute:

  • Zero people get in line 30% of the time

  • One person gets in line 40% of the time

  • Two people get in line 30% of the time

    Using this system we can find the expected wait time per customer and the expected line length they will encounter.


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Problem analysis

  • We generated random numbers in Excel and used a program written by Tiffany to run the experiment

  • We want to explore:

    Ho: Mx = My

    H1: Mx > My


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Results

  • We reject the null hypothesis in favor of the alternative hypothesis. This shows that the average wait time for a one-lane system is longer than a two-lane system.

  • Therefore, we would choose a two-lane system to effectively lower the wait time for customers.


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Questions

  • Under what circumstances would you use the Monte Carlo Simulation?

  • Name three ways you can generate random numbers.


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