Integrating Normal Distributions gives the wrong answer

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Integrating Normal Distributions gives the wrong answer*From*: mek at guinan.psu.edu (Mark E. Kotanchek)*Date*: Tue, 8 Sep 92 16:58:04 EDT

I was intending to as y'all about the suitability of running Mma 2.1 on a Mac Powerbook 170 since I was working at home over the weekend trying to figure out convergence rates of covariance matrices; alas, now that I'm playing with Mma 2.0 on my office NeXTstation, I'm wondering whether I should spring for Maple and avoid the "beautifully formatted, incorrect answers" syndrome which my colleague is chortling about at the moment. The issue is integrating normal distribution functions. Given that I define the Gaussian density function, f=Exp[-(x-mu)^2/(2 sigma^2)]/(sigma Sqrt[2 Pi]) which gives me 1 --------------------------------------- 2 2 (-mu + x) /(2 sigma ) E Sqrt[2 Pi] sigma upon integrating from negative to positive infinity I should get a result of 1. Instead Mathematica assures me that the answer is zero!! Integrate[f,{x,-Infinity,Infinity}] 0 Setting mu = 0 leads to the result, mu=0; Integrate[f,{x,-Infinity,Infinity}] sigma ---------- Abs[sigma] which, is closer and presumably Mathematica would give me the correct result if I knew how to tell Mathematica that sigma is always non-negative. (A feature which I'm sure must be in Mathematica but manages to elude me while scouring Blachman's various books and Wolfram's manual--obtuse documentation of an obtuse program overcomes me once more!) Anyhow, is this misbehavior of Mathematica fixed in v2.1 or is there some sort of a rationale for such behavior? It seems like I'm trying such a simple exercise that there isn't much room for operator error.... Thanks much, Mark. --- Mark Kotanchek Guidance & Control Dept - 363 ASB Applied Research Lab/Penn State P.O. Box 30 State College, PA 16804 e-mail: mek at guinan.psu.edu (NeXTmail) TEL: (814)863-0682 FAX: (814)863-7843