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 (previous estimate of a range of limit values). These methods are especially good for optimization and numerical integration in 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 distribution (see the following figure) but there are other distributions such as geometric or Poisson.