Consider the function f(x) = 3x3 2 1 x 1 0 otherwise
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Consider the function f(x) =
⎧
⎨
⎩
3x3 2 −1 ≤ x ≤ 1 0 otherwise Suggest a probability density function π(x), where −1 ≤ x ≤ 1, and a function h(x) such that we can obtain the following Monte Carlo integration:
1
−1 f(x)dx =
1
−1 h(x)π(x)dx = Eπ[h(x)]∼= 1 n
n k=1 h(xk)
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