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MathGroup Archive 1992

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Re: Integrating Normal Distributions gives the wrong answer

  • To: mathgroup at
  • Subject: Re: Integrating Normal Distributions gives the wrong answer
  • From: mek at (Mark E. Kotanchek)
  • Date: Wed, 16 Sep 92 14:17:52 EDT


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  

In any case, if I execute


I get an answer of


rather than the expected "1". Following the discussion of "Adding a  
conditional def to Sqrt", I implemented

   Sqrt[x_^y_] := x^(y/2)/;EvenQ[y];
   Power[x_^y_,z_] := x^(y/2) /; EvenQ[y] && z==1/2;

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  


Mark Kotanchek
Guidance & Control Dept - 363 ASB
Applied Research Lab/Penn State
P.O. Box 30
State College, PA 16804

e-mail:	mek at (NeXTmail)
TEL:	(814)863-0682
FAX:	(814)863-7843

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