In this chapter, we addressed the basic concepts of Monte Carlo simulation. We explored the Monte Carlo components used to obtain a simulation with satisfactory results. Hence, we used Monte Carlo methods to estimate the value of pi.
We then tackled two fundamental concepts of Monte Carlo simulation: the law of large numbers and the central limit theorem. For example, the law of large numbers allows us to determine the centers and weights of a Monte Carlo analysis for the estimate of definite integrals. The central limit theorem is of great importance and it is thanks to this that many statistical procedures work.
Next, we analyzed practical applications of using Monte Carlo methods in real life: numerical optimization and project management. Finally, we learned how to perform numerical integration using Monte Carlo techniques.
In the next chapter, we will learn the basic concepts of the Markov process. We will understand the agent-environment interaction process...