What is Monte Carlo algorithm?
[[File:Pi 30K.gif|thumb|Monte Carlo method applied to [[approximation|approximating]] the value of [[Pi (mathematics)|π]]. After placing 30,000 random points, the probability that the estimate for π is within 0.07% of the actual value.]] A '''Monte Carlo algorithm''' is an [[algorithm]] for [[computer]]s which is used to [[simulation|simulate]] the [[wikt:behaviour|behaviour]] of other systems. It is not an exact method, but a [[heuristics|heuristical]] one, typically using [[random]]ness and [[statistics]] to get a result. The algorithm terminates with an answer that is correct with probability <math>p<1</math>. It is a [[computation]] process that uses random numbers to produce an outcome(s). Instead of having fixed inputs, [[probability distribution]]s are assigned to some or all of the inputs. This will generate a probability distribution for the output after the simulation is run. For example, a Monte Carlo algorithm can be used to estimate the value of [[Pi (mathematics)|π]]. The amount of area within a quarter-circle of radius 1 depends on the value of [[Pi (mathematics)|π]]. The [[probability]] that a randomly-chosen point will lie in that quarter-circle depends on the area of the circle. If points are placed randomly in a square with sides of length 1, the [[percentage]] of points that fall within a quarter-circle of radius 1 will depend on the value of [[Pi (mathematics)|π]]. A Monte Carlo algorithm would randomly place points in the square and use the percentage of points falling inside of the circle to estimate the value of [[Pi (mathematics)|π]].This is an effective way for making approximations. In modern [[communication]] systems, the quality of information exchange is determined by the presence of noise in the channel. The major source of noise - Additive White [[Normal distribution|Gaussian]] Noise (AWGN) being random in nature can be characterized using the Monte Carlo algorithm in simulating a Communications System The modern version of the [[Markov chain]] Monte Carlo method was invented