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Integral I:
Estimator for I:
where f(x) = 20 - x^2 and p(x) ~ U[a,b]
Create a Python function for I-Antithetic
def montecarlo_antithetic (f: Callable [[float], [float]], a: float, b: float, n:int):
returnInAntithetic=n/21i=1n/221(p(xi)f(xi)+p(x^i)f(x^i))(InAntithetic,Var(InAntithetic))p(x)={b
a1,0,x[a,b]otherwiseI=abf(x)dx

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Integral IEstimator for Iwhere f(x) = 20 - x^2 and p(x) ~ U[a,.pdf

  • 1. Integral I: Estimator for I: where f(x) = 20 - x^2 and p(x) ~ U[a,b] Create a Python function for I-Antithetic def montecarlo_antithetic (f: Callable [[float], [float]], a: float, b: float, n:int): returnInAntithetic=n/21i=1n/221(p(xi)f(xi)+p(x^i)f(x^i))(InAntithetic,Var(InAntithetic))p(x)={b a1,0,x[a,b]otherwiseI=abf(x)dx