Monte Carlo Integration
Estimate the integral of a function over a hyper-rectangle using Monte Carlo sampling. Particularly effective for high-dimensional integrals where traditional methods suffer from the curse of dimensionality. Returns both the integral estimate and standard error, allowing confidence interval construction. Essential for option pricing, risk calculations, and multidimensional probability computations. [Tier: BASIC, Credits: 1]
Authorizations
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Body
Built-in function (multi-variable for multi-d, scalar for 1-d)
rosenbrock, sphere, rastrigin, quadratic, exp, sin, cos "sphere"
Integration bounds for each dimension [[a1,b1], [a2,b2], ...]
2 elements[[-1, 1], [-1, 1]]Number of Monte Carlo samples (more samples = more accurate)
10000
Random seed for reproducibility
42
