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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[39]:=
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[37]=
2
M sigma
----------- <------ should be "M sigma"
1 M/2 M/2
(-) 2
2
Out[38]=
4
M (2 + M) sigma
----------------
1 M/2 M/2
(-) 2
2
Out[39]=
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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