       Failure to recognize "1"

• To: mathgroup at yoda.physics.unc.edu
• Subject: Failure to recognize "1"
• From: mek at guinan.psu.edu (Mark E. Kotanchek)
• Date: Wed, 8 Sep 93 21:57:54 -0400

```Hi,

I'm currently working with the average of the autocovariance of a Gaussian
random variable. Hence, I defined the function

fChi2[R2_,sigma_,N_] := PDF[ChiSquareDistribution[N],R2/(sigma^2)]/sigma^2

which is the density function for a chi-squared distribution in the
non-normalized case. (The Mma function presumes a standard deviation of 1.)
Anyhow, given my hard won suspicion of Mma integrals, I checked the expected
value and standard deviation. Running Mma 2.1 on my NeXTstation I got,

In:=
Declare[sigma, NonNegative]
Declare[sigma, Real]
Declare[M, Positive]
expectedAvg = Integrate[R2 fChi2[R2,sigma,M],{R2,0,Infinity}]
secondMoment = Integrate[R2^2 fChi2[R2,sigma,M],{R2,0,Infinity}]
stdDeviation = Sqrt[secondMoment - expectedAvg^2]

Out=
2
M sigma
-----------   <------ should be "M sigma"
1 M/2  M/2
(-)    2
2

Out=
4
M (2 + M) sigma
----------------
1 M/2  M/2
(-)    2
2

Out=
2      4                   4
M  sigma     M (2 + M) sigma
Sqrt[-(---------) + ----------------] <-- Sqrt[2 M] sigma^2
1 M  M        1 M/2  M/2
(-)  2        (-)    2
2             2

My question is why Mma doesn't recognize that

1 M/2  M/2
(-)    2      = "1"?
2

As a result, the above equation doesn't simplify upon application of simplify
or expand. Is there some subtlety I'm missing or is this a bug in 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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