Importance Sampling Problem

I'm currently stuck on a problem that I can't seem to get my head around. Here it is:

Let X,Y~N(0,1) be independent.

Explain how importnace sampling, with samples from X_{1}~N(mu_{x},1) and Y_{1}~N(mu_{y},1), can be used to estimate the probability p(c)= P(XY>=c, X>=0). Discuss how mu_{x} and mu_{y} should be chosen in order for the importance sampling method to be efficeint.

Any help is much appreciated.

Re: Importance Sampling Problem

Hey Mullineux.

In terms of the technique, consider an indicator variable for Z = XY if XY >= c and then find E[Z;X>=0].

You can use the fact that the probability will correspond to a Bernoulli distribution where if I[Z] = 0 if XY < c and 1 if XY >=c then E[I[Z]] = P(XY >= c).