Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1992
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1992

[Date Index] [Thread Index] [Author Index]

Search the Archive

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





  • Prev by Date: Has someone a Simplify that really simplifies?
  • Next by Date: Re: Can MMa run on a NeXT with 8Mbyte?
  • Previous by thread: Re: Integrating Normal Distributions gives the wrong answer
  • Next by thread: Re: Integrating Normal Distributions gives the wrong answer