Monte Carlo Integration

Monte Carlo methods can be thought of as statistical simulation methods that utilize a sequences of random numbers to perform the simulation. The name “Monte Carlo” was coined by Nicholas Constantine Metropolis (1915-1999) and inspired by Stanslaw Ulam (1909-1986), because of the similarity of statistical simulation to games of chance, and because Monte Carlo is a center for gambling and games of chance.

The Monte Carlo method can be used to numerically approximate the value of an integral.  For a function of one variable the steps are:

Hasil integral Monte Carlo dengan N = 20 adalah 166,07. Hasil ini lebih mendekati hasil analitik dari pada hasil integral Monte Carlo dengan N = 5. Hal ini menunjukkan bahwa semakin banyak bilangan acak yang dibangkitkan hasilnya akan mendekati solusi analitik

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