Re: Integrating Normal Distributions gives the wrong answer

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Re: Integrating Normal Distributions gives the wrong answer*From*: mek at guinan.psu.edu (Mark E. Kotanchek)*Date*: Wed, 16 Sep 92 14:17:52 EDT

Howdy, Thanks to Gordon, Charlie, Steve, Pat, Tom, and Jason for confirming the misbehavior of Mma w.r.t. integration. I've ordered the 2.1 upgrade and am eagerly waiting to integrate properly (and stop my colleague next door from chortling about the relative merits of Maple). In any case, if I execute mu=0; Integrate[PDF[NormalDistribution[mu,sigma],x],{x,-Infinity,Infinit y}] I get an answer of sigma ---------- Abs[sigma] rather than the expected "1". Following the discussion of "Adding a conditional def to Sqrt", I implemented Unprotect[Sqrt]; Sqrt[x_^y_] := x^(y/2)/;EvenQ[y]; Protect[Sqrt]; Unprotect[Power]; Power[x_^y_,z_] := x^(y/2) /; EvenQ[y] && z==1/2; Protect[Power]; after which I got the desired result of "1". I don't know WHY this worked and was wondering if y'all could explain it and whether v2.1 has such a "fix" implented or whether I need to remember to execute this sequence every time I wanted to do symbolic computations.... This leads me in the question of how to define bounds on a variable. For example, if "theta" is defined to exist on the between -Pi/2 and Pi/2, how do I tell Mma this? In this case I would expect "ArcSin[Sin[z]]" to simplify to "z" rather than "ArcSin[Sin[z]]". I've tried looking through Blachman's books, the manual, the tutorials, etc. under the headings {conditionals, limits, boundaries, ..., etc.} but nothing so far has raised a detection flag. Is there another book or files someplace wherein an ignorant soul like myself could learn such things or do I simply have to get into the karma of Mma? Thanks, 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