$\displaystyle I(f)=\int_{a}^{b}=f(x)dx$

g is a density function on [a, b]. $\displaystyle X_{1}, X_{2},... X_{n}$ are generated by $\displaystyle \hat{I}(f)=\frac{1}{n} \sum{\frac{f(X)}{g(X)}}$.

How do I get $\displaystyle Var(\hat{I}(f))$?

Printable View

- Mar 4th 2010, 01:52 PMbrogersmonte carlo method
$\displaystyle I(f)=\int_{a}^{b}=f(x)dx$

g is a density function on [a, b]. $\displaystyle X_{1}, X_{2},... X_{n}$ are generated by $\displaystyle \hat{I}(f)=\frac{1}{n} \sum{\frac{f(X)}{g(X)}}$.

How do I get $\displaystyle Var(\hat{I}(f))$?