integrating a bivariate normal

*To*: mathgroup at smc.vnet.net*Subject*: [mg13704] integrating a bivariate normal*From*: Dennis Swaney <dennis at shrubbery.com>*Date*: Wed, 19 Aug 1998 01:38:02 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Dear Mathgroup- Is it me, or is Mathematica incapable of integrating the bivariate normal distribution if the variables are correlated? First, I tried the following (integrating the pdf for uncorrelated variables): Integrate[Exp[-1/2*(((x - m1)/s1 )^2 + ((y - m2)/s2)^2)]/(2*Pi*Sqrt[s1^2]* Sqrt[s2^2]), {x, -Infinity, Infinity}, {y, -Infinity, Infinity}] and it produced the correct answer (1). Next, I tried integrating the pdf for nonzero r: Integrate[Exp[-1/(2(1-r^2))*(((x - m1)/s1 )^2 + ((y - m2)/s2)^2-2 r((x - m1)/s1 ) ((y - m2)/s2 ))]/( 2*Pi*Sqrt[s1^2]* Sqrt[s2^2]*Sqrt[1-r^2]), {x, -Infinity, Infinity}, {y, -Infinity, Infinity}] and it produced a long, erroneous result (a function of x, which is a variable of integration!) Is it possible that the problem results because Abs(r) should be < 1? If so, how can I specify this condition? thanks -Dennis Dennis P. Swaney email: Dennis at shrubbery.com