This page addresses the case that occurs for many real world applications of Monte Carlo simulation where there is more than one variable and/or some or all of the variables have correlation. If the variables do not have mean reversion, the Cholesky function can be used. But in other cases this does not work. Monte Carlo simulation is also use do demonstrate how the means square error works when there are multiple variables.
Demonstration of Mean Squared Error
If you have multiple variables and want to compute the standard deviation, you cannot simply add-up the standard deviation and come up with the total standard deviation for the series. Instead, you can compute the variation of each series, then add-up the variation (the square of the standard deviation) and finally, you compute the square root of the sum of the standard deviations.
The file below demonstrates how you can prove that the MSE equation works using Monte Carlo Simulation.