Monte Carlo methods are the techniques which used in computing estimates via sampling. These methods are highly used within the range from estimating of a intractable integral to system simulation. Here, I’ll try to give some initial ideas with the help of the illustration of some basic techniques.
We can start with inversion method. The key idea of it is that when $f_X$ is the probability density of the random variable $X$, the cumulative density function (CDF) $F_X(X)$ is uniformly distributed on [0, 1) when viewed as a random variable.