Article View: sci.math.stat
Article #630Re: Variance of AxB?
From: Herman Rubin
Date: Sat, 03 Oct 1992 14:42
Date: Sat, 03 Oct 1992 14:42
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1477 bytes
In article <23788@alice.att.com> rhh@alice.att.com (r hardin) writes:
>I seem to remember a handy trick for normal distributed numbers,
>the expected value of any product of them <abcd> say is
><abcd> = <ab> <cd> + <ac> <bd> + <ad> <bc>
>ie., just write every unique product of pairs
>which works for any order of product.
>From which, if I have remembered it correctly of course, you can
>compute any variance.
>Perhaps someone can verify the rule, which I am remembering from
>a distance of perhaps 20 years.
The rule is correct if the random variables have mean 0, and is
easily obtained by differentiating the moment generating function
the appropriate number of times and seeing which terms are not 0.
It is not valid if the means are not 0.
--
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
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Path: arc1-ca.pugleaf.net!sparky!uunet!haven.umd.edu!darwin.sura.net!zaphod.mps.ohio-state.edu!pacific.mps.ohio-state.edu!linac!att!news.cs.indiana.edu!purdue!mentor.cc.purdue.edu!hrubin From: hrubin@mentor.cc.purdue.edu (Herman Rubin) Newsgroups: sci.math.stat Subject: Re: Variance of AxB? Message-ID: <BvJvIC.4Cn@mentor.cc.purdue.edu> Date: 3 Oct 92 14:42:12 GMT References: <1992Oct1.211244.259299@ns1.cc.lehigh.edu> <23788@alice.att.com> Organization: Purdue University Statistics Department Lines: 29