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Math Help - Importance Sampling Problem

  1. #1
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    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 X1~N(mux,1) and Y1~N(muy,1), can be used to estimate the probability p(c)= P(XY>=c, X>=0). Discuss how mux and muy should be chosen in order for the importance sampling method to be efficeint.

    Any help is much appreciated.
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  2. #2
    MHF Contributor
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    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).
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