Monte Carlo integration is a method to numerically estimate integral like I(g) = Sa g(x)dx. The idea is to sample X1, X2, . This problem introduces a variation on the Monte Carlo integration technique. Let h(x) be a density function on [a, b]. Generate X1,..., Xn independently from h(x) and estimate I(g) by Î(g) = 1 Xn independent Unif(a, b) and estimate I(g) as E1 9(X;). ... g(X;) i=1 h(X;)* n (a) Show that E[Ï(g)] = I(g).

Monte Carlo integration is a method to numerically estimate integral like I(g) = Sa g(x)dx. The idea is to sample X1, X2, . This problem introduces a variation on the Monte Carlo integration technique. Let h(x) be a density function on [a, b]. Generate X1,..., Xn independently from h(x) and estimate I(g) by Î(g) = 1 Xn independent Unif(a, b) and estimate I(g) as E1 9(X;). ... g(X;) i=1 h(X;)* n (a) Show that E[Ï(g)] = I(g).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.3: Maxima And Minima

Problem 20E

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