Simple Monte Carlo Integration Example

Lower limit

A = 0

Upper limit

B = 1

Number of samples

N = 100

Function to integrate

f (x) = x^{3}

Foreign function interface

ξ = drand48

Sample value

x_{i} = A + (B - A) ξ_{}

Approximation to integral

Integral = \frac{1}{N} \sum_{i = 1}^{N} f (x_{i})

Variance in approximation to integral

Variance = \frac{1}{N} \sum_{i = 1}^{N} {f (x_{i})}^{2} - {(\frac{1}{N} \sum_{i = 1}^{N} f (x_{i}))}^{2}

Standard error in approximation to integral

StandardError = \sqrt{\frac{Variance}{(N - 1)}}