# Probability, Distribution, and Simulation

## Initial Post

### Part A: Simulation

Simulation in Excel is a simple task that does not require much time. If one needs to simulate random values, he or she may use simple functions of RAND or RANDBETWEEN functions. RAND function provides a number between 0 and 1 with a low probability of repetition, while RANDBETWEEN will give a discrete value between the entered numbers with a high likelihood of recurrence (How to generate random numbers in Excel, n.d.). Even though these two functions are the easiest ways to generate a random number, they are irrelevant to the present problem.

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In order to generate 500 random numbers using the provided probability table, a random number generator needs to be used. Therefore, I went to the Data Analysis menu and pressed Random Number Generator. After that, I entered “1” in the Number of variables, “500” in the Number of Random Numbers, selected “Discrete” for distribution, and entered value and probability input range. Please, refer to the attached Excel file for the results of the simulation.

### Part B: Simulation Analysis

The calculation of the mean and standard deviation (SD) of the simulated values is straightforward. The AVG function should be used for calculating the mean, and STDEV is to be used for SD. The mean of the simulation was 1.53, while SD was 1.18. The mean and SD of the probability distribution table were calculated manually, using the formula mentioned by Albright and Winston (2017). Please, refer to the attached Excel file for the calculations. The results were slightly different from the simulated results since the mean was 1.5, and SD was 1.16.

## Guided Response

### Proposed Tips

1. Finding standard the mean deviation of a discrete random variable may be a complicated task since there are no built-in functions to do so. Therefore, I suggest watching a YouTube video to master the skill.
2. When making a simulation, the random number generator will automatically put the result on a separate spreadsheet. If you find it inconvenient, you can alter the output options by manually selecting the output range before the simulation.

## References

Albright, C., & Winston, W. (2017). Business Analytics (6th ed.). Web.

How to generate random numbers in Excel. (n.d.). Web.

Hays, D. (2012). Excel 2010: Mean, standard deviation, and variance of a discrete random variable [Video File]. Web.

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