I need two comments, each part is around 150 words.

Part 1:

**Explain how Monte Carlo simulation is used by enterprises in the real world. Provide a specific example from your own line of work, or a line of work that you find particularly interesting. Remember that any proper explanation of a Monte Carlo simulation would involve describing the probability distributions that have been utilized in that simulation.**

Monto Carlo simulations are a great tool being frequently employed by numerous enterprises in the real world today. The simulation is useful to make decisions based on historical data, which generates a probability of an event occurring based on a large number of future samples.

For example, let’s say we want to know the probability that the return of a particular stock (i.e. Microsoft) is going to be greater than 2.5%. First, we get the mean and standard deviation of the stock’s return, based on the data gathered in the last 5 years. However, it would be beneficial to have access to data from greater than 5 years, if that is possible.

Then, in Excel, we use the NORMINV() function to calculate the inverse of the Cumulative Normal Distribution function for a given probability value, using the historical mean and standard deviation values. RAND() is thenset to generate random numbers between 0 and 1 for the probability, in addition to the historic mean and standard deviation values.

Eventually, we generate the expected return for the stock for each of the next 10,000 days. Let’s keep this figure for the purpose of this example, however we recommend to increase this value even more. Finally, we compute the percent of times Microsoft’s stock was 2.5% or greater over the rows of data that we generated in our simulation.

Based on this, we can evaluate whether we should invest in Microsoft, or instead look for a stock to buy that may provide a greater return. Used correctly, financial advisors are able to leverage the power of Monte Carlo simulations, and make more informed decisions for their clients.

**Identify that parts or aspects of Monte Carlo simulation processes that you have found to be particularly challenging. Describe why you believe that they are challenging and provide remedies to simplify those aspects.**

There are various aspects of Monte Carlo simulations that might pose a challenge. For example, not having enough historical data could be problematic. Since Monte Carlo simulations depend on historical data, having enough data is essential. The historical data is what provides the mean and standard deviation values, which are inputted in to the NORMINV() function, to generate a predicted value.

Fortunately, we can correct this error, by including at least 5 years worth of historical data in our model. If we are able to get access to an online database with Microsoft’s financial information over the last 5 years, our simulation would be prone to less errors.

Also, not running the Monte Carlo simulation enough can lead to errors in the predicted values. For example, running the Monte Carlo simulation only 100 times, as opposed to 10,000 times, may not be the best use of the simulation. As a result, the data being predicted may not be entirely accurate, and in doing so, would lead to decisions that could turn out to be flawed and ill-informed.

However, we can counteract this negative effect, by increasing the simulation trial to 10,000 times, for example. A larger simulation trial would, therefore, provide more predictive data to the model, resulting in extremely well-informed decisions taken by the financial advisors for their clients. By doing so, they would be able to compute the percent of times Microsoft’s stock was 2.5% or greater, and understand the risk in buying the stock if the probability met their individual needs.

Part 2:

**Explain how Monte Carlo simulation is used by enterprises in the real world. Provide a specific example from your own line of work, or a line of work that you find particularly interesting. Remember that any proper explanation of a Monte Carlo simulation would involve describing the probability distributions that have been utilized in that simulation.**

Many large enterprises utilize Monte Carlo simulation to make informed decisions that are based on random sampling based on past historical data. Simulations can be useful for both private and public institutions, such as the US Army, where a Monte Carlo simulation was used to determine if current modeling estimates of Air Ambulance demands was in line with historical data from Operation Iraqi Freedom (OIF)(Fulton 2009). The issue here is that if current Army modelling is not allocating enough resources to a specific action, such as Air Ambulances, then Army decision makers, who often use the Total Army Analysis (TAA) process to determine resource allocation, will not have a clear picture of the Army Force Structure required to meet the demands of a potential future fight. From the attached paper, ““TAA develops requirements and authorizations defining the force structure the Army must build, raise, provision, sustain, maintain, train, and resource(Fulton 2009).” If the models underpinning this analysis do not accurately model demand, then the Army will be short resources in the future. From the paper the current models was an existence rule, meaning that one Ambulance type unit was allocated in modeling per type of area. The paper argues, through the use of Monte Carlo simulation, that this underestimates the demand. The Historical data for this simulation had a triangular distribution that was utilized with a minimum of 0.5, mode of 1, and a maximum of 4 hours. The conclusion of the report was that “If small units are subordinate to an entity (e.g., a battalion) that does not share the same demand characteristics, leaders should consider evaluating these units’ requirements separately,” suggesting that modelling based on historical workload is a more “reasonable” approach than the TAA process in 2009(Fulton 2009).

Fulton L, McMurry P, Kerr B. A Monte Carlo simulation of air ambulance requirements during major combat operations. Mil Med. 2009 Jun;174(6):610-4. doi: 10.7205/milmed-d-02-0208. PMID: 19585774.

**Identify that parts or aspects of Monte Carlo simulation processes that you have found to be particularly challenging. Describe why you believe that they are challenging and provide remedies to simplify those aspects.**

I have never utilized Monte Carlo Simulation in my work, but from the paper I found two potential areas that the authors may have struggled with.

From the above example there are several areas where the use of a Monte Carlo simulation may have had trouble. As this paper was written in 2009, the data collection of the war had not finished, and this ongoing conflict may change their input if it were performed later. Similarly, an increase in the amount of data points utilized to calculate the distribution would strengthen the application of this simulation. Conversely, sticking to a time period that may provide a more accurate depiction of future conflicts could increase the likelihood that the simulation was meaningful, and that future leaders could depend on these results.

Another interesting take away from the paper was that “250 runs provided the estimates for evaluation,” which seems on the low side based on the technical capabilities out there (Fulton 2009). While time is often the constraint for the number of simulations run, this limited number of runs may have skewed their results in one direction. By increasing the number of runs, the authors may have been able to provide a more accurate estimation for future conflicts that could better inform decision makers on how to resource the Army’s force structure and manning.