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}]

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

```

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