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I am trying to understand the bivariate normal distribution. If I have X and Y normally distributed, with means and standard deviations given for each, and a correlation coefficient also given, how would I express Y in terms of a multiple of X and a term which is independent of X?

I see that you can express Y in terms of Y= (standard deviation of Y)Z + (mean of Y), where Z is normally distributed, and similar for X, but I do not see a) how to include the correlation coefficient, and know whether it is legitimate to simply replace the variable Z in the equation for Y with another generic standard normally distributed variable, say Z2?

Thanks.

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