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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

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

- 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

Pros

- Easy to use
- Can make the complex data simple
- Does not take a lot of time to analyze
- Inexpensive

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

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.

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.

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.

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

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.

Questions

- Under what circumstances would you use the Monte Carlo Simulation?
- Name three ways you can generate random numbers.

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