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I want to do numerical integration of some functions using the Monte Carlo method. The default setting for the Monte Carlo method is to use a uniform distribution as far as I know.

How can I change the random number generation to Gaussian when doing numerical integration?

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You can look up the examples here. –  b.gatessucks Apr 1 '14 at 9:00
If you can figure out the PointGenerator option for MonteCarloRule, I think that's a path. Zero documentation of it (at least as far as I've seen) other than the mention in the advanced numerical integration tutorial docs. –  rasher Apr 1 '14 at 10:08
Attempting to use the mentioned but undocumented sub-option "PointGenerator" of option Method of NIntegrate can be dangerous to your kernel. At least, my attempts to set this sub-option anything other than its default resulted in a kernel crash. –  m_goldberg Apr 1 '14 at 11:08
why don't you implement it yourself? There is a mathematica example on the wiki page by the way en.wikipedia.org/wiki/Monte_Carlo_integration. (I didn't study it but it looks like a good start ) –  george2079 Apr 1 '14 at 12:48

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