Question: Explain how importance sampling can improve the efficiency of a simple Monte Carlo algorithm.

Answer so far:

I have done all the integration proof showing how you mutliply by h(x) / h(x) which is 1, given the properties of a good improtance sampling function, and given a small example of how you move the mean so you can have more samples of the required value.

Having feedback from my teacher he now says i should explain how the density(importance) ratio f(x) / h(x) is used here in the monte carlo approximation!

Now i am confused...any help would be great!

Thanks

Ben