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Monte Carlo integration, simple example

What we are doing is to employ a random number generator to obtain numbers x_i in the interval [0,1] through a call to one of the library functions ran0 , ran1 , ran2 or ran3 which generate random numbers in the interval x\in [0,1] . These functions will be discussed in the next section. Here we simply employ these functions in order to generate a random variable. All random number generators produce pseudo-random numbers in the interval [0,1] using the so-called uniform probability distribution p(x) defined as \begin{equation*} p(x)=\frac{1}{b-a}\Theta(x-a)\Theta(b-x), \end{equation*} with a=0 og b=1 and where \Theta is the standard Heaviside function or simply the step function.