The result is a vector of thousands of equally likely results. MC goes repeatedly through the same process, but each "cycle" uses different random choices from the input variables. One of the advances of the MC methods is that the mechanism is easier to explain than a rather complicated math solution. The results will never be exact but good enough for the purpose. Now, many problems of combining distributions, or simulating stochastic processes can be done through Monte Carlo methods ( MC) without great costs in computer time. In the past, when main frame computers had a RAM of a few K, statisticians and mathematicians tried their utmost best to find analytical solutions to stachastic problems. Simulating correlation between MC vectors.Prediction based on a regression equation. Generating analytical distributions in MC.
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