Simulations

Overview

Simulations are a way to approximately compute the statistics areound a give process or distribution when you dont know how to derive an analytical formula for that statistic. For example, lets say you wanted to know what the standard deviation of a coin flip was. If you didnt know the formula, but you did have a program that generated 0s and 1s with a 50% probability each, you could just generate a large number of 0s and 1s and take the standard deviation of the result. This would give you a number which would be approximately the true distributions standard deviation.

Topics

• Simulating a Uniform Distribution
• Simulating Other Distributions
• Plotting Simulated Distributions
• Simulating Multi Variable Distributions : any problems involve more than one variable. In these cases, we need a method to generate variables from a given multivariable distribution. If the variables are independent, then we can get generate them separately. However, independent variables are rare.
• Simulating Time Series
• Solving Integration Problems with Monte Carlo

Randomly Generated Numbers

The following is a graph of randomly generated numbers, (x,y), where x is generated from the uniform distribution from [-1,1] and y is generated from the uniform distribution.



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