Consider the function f(x) = 3x3 2 1 x 1 0 otherwise Suggest a probability density function (x), where 1

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)