Monte Carlo methods

Random Walk is a member of a family of random sampling algorithms. Proposed by Stanislaw Ulam in 1940, Monte Carlo methods are mainly used when the event has uncertainty and deterministic boundaries (the previous estimate was for a range of limit values). These methods are especially good for optimization and numerical integration in finance, biology, business, physics, and statistics.

Monte Carlo methods depend on the probability distribution of the random number generator to see different behaviors in the simulations. The most common distribution is the Gauss or Normal; this distribution is also referred to as Bell Curve (see the following diagram), but there are more distributions such as the Geometric or Poisson. In statistics, the Central Limit Theorem (CTL) proposes that the Gaussian distribution will appear in almost any case. Where the sample of n elements from a uniform random source (if the number of samples gets larger, the approximation improves), the sum of...