Newsgroup sci.stat.math 12457

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I am guessing, not well at all.  There must surely be an infinite number 
of distributions with the same first four moments?
However, if you are willing to assume that your distribution belongs to 
given set, e.g., Pearson's system, then all the percentages would be
known.
Reference:
Elderton, William Palin, 1953, Frequency Curves and Correlation
   Washington DC, Harren Press, 272 p.
-- 
Gerry Middleton
Department of Geology, McMaster University
Tel: (905) 525-9140 ext 24187 FAX 522-3141

If you are interested in acquiring inexpensive Statistical Analysis
Software contact RCKnodt@aol.com.  Great for business students taking stat
or anyone involved in research.

In article <5bsc70$f1d@csu-b.csuohio.edu> drake.79@osu.edu (Macarthur Drake) writes:
>This messege is to provoke a serious scientific debate.
>        I am an engineer, no biologist, astronomer or statictician or 
>anything, but something puzzles me. I am sure you are aware of the Late Dr. 
>Sagan's quote  " extraordinary claims require extraordinary proof " with 
>regards to extraterrestrial life, UFOs etc. I have also heard people say 
>that the discovery of life on another world would be the greatest discovery 
>in human history.
The first man on the moon was supposed to be the greatest event of the 
century, but so far it has impacted my life a lot less than the OJ trial or my 
grand-daughter's birthday.
What if the aliens turned out to be incredibly boring bureaucrats, or 
religious fruitcakes, or spoiled rock stars, or sullen Gen-X'ers?  We'd soon 
be looking for some way to un-discover them.
In any case, the unambiguous discovery of life elsewhere in the universe would 
get about 1 column in the Chicago Tribune, if no aldermen were being indicted 
that day, and about 1/4 page in People magazine.  Congress would probably pass 
a bill restricting immigration of aliens to the US, and restaurant owners 
would make the case that antidiscrimination laws did not apply to 
neodymium-based life forms.  Other than that, the whole thing would be a big 
yawn, on the worldwide scale.
>                        Logical and insightfully comments welcomed!
Sure, here's a comment:  Next time, don't spam every newsgroup in the known 
universe with your deathless observations.
Bill
********************************************************
Bill Penrose, President, Custom Sensor Solutions, Inc.
526 West Franklin Avenue, Naperville, IL 60540
630-548-3548, fax: 630-369-9618
email wpenrose@interaccess.com
********************************************************

In article <5bsc70$f1d@csu-b.csuohio.edu> drake.79@osu.edu (Macarthur Drake) writes:
>        I am an engineer, no biologist, astronomer or statictician or 
>anything, but something puzzles me. I am sure you are aware of the Late Dr. 
>Sagan's quote  " extraordinary claims require extraordinary proof " with 
>regards to extraterrestrial life, UFOs etc. I have also heard people say 
>that the discovery of life on another world would be the greatest discovery 
>in human history.
The first man on the moon was supposed to be the event of the century.  While 
exciting at the time, its net effect on my life has been a lot less than my 
dog throwing up on the living room rug, my grand-daughter's birthday, or even 
the OJ trial.  Same goes for "life" on Mars.
The discovery of extraterrestrial intelligence would get about 1 column in the 
Chicago Tribune, provided that no aldermen were being indicted that day, and 
about 1/4 page in People Magazine, provided there were pictures.  Congress 
would pass a law prohibiting immigration from other star systems, and a
restaurant chain would claim that the antidiscrimination laws do not apply to 
neodymium-based life forms.  Otherwise, there would be a world-wide, 
collective yawn.
>                        
>                        Logical and insightfully comments welcomed!
Here's a comment:  Was this so important that it had to be spammed to 
"billions and billions" of newsgroups?
Bill
(If this post nearly duplicates a previous one of mine, it is because my 
provider lost it after posting and the original may yet find its way to the 
ng.)
********************************************************
Bill Penrose, President, Custom Sensor Solutions, Inc.
526 West Franklin Avenue, Naperville, IL 60540
630-548-3548, fax: 630-369-9618
email wpenrose@interaccess.com
********************************************************

Macarthur Drake wrote:
> 
> This messege is to provoke a serious scientific debate.
> **********contents snipped**********
Agreed! I seem to remember Isaac Asimov coming down to a number of
carbon-based life-holding-planets to be a number with so many places
that a human could not write it down in a lifetime.
Then of course there is the "WHEN" to take into account, as well as the
"WHERE".
Cary (a layman)

hi,
I have the following question on my statistics 
assignment and Im not sure how to go about 
solving it :
S^2 is the variance of a random sample of size 
n from a N(mu,sigma^2) population.
Prove that 
 g = n S^2/ (n-1) converges in probability to 
     sigma^2.
Im not sure how to go about solving this problem.
I know  nS^2/sigma^2 ~ Chi-squared (n-1), using
this and the approp. transformation I can get 
the density function for g. Is this the right 
approach or am I missing something.
thanks,
roger

Macarthur Drake  wrote:
> This messege is to provoke a serious scientific debate.
Then it should have been written more seriously and without
a plethora of spelling and grammatical errors!!
> I am an engineer, no biologist, astronomer or statictician or anything,
> but something puzzles me. I am sure you are aware of the Late Dr. 
> Sagan's quote  " extraordinary claims require extraordinary proof "
> with regards to extraterrestrial life, UFOs etc.  I have also heard
> people say that the discovery of life on another world would be the 
> greatest discovery in human history.
> I beg to differ with both of these ridiculus statments.
> [snip]
> I would appriciate any math or stats expert to comment on the 
> chances that we are alone in the entire universe. I bet that s/he'd 
> say that it is statistically impossible for us to be alone, so what's 
> the big deal we know that life is there, just a matter of time 'til
> we find it....or them us!
> [snip - again]
Extraordinary claims DO REQUIRE extraordinary proof.  Statistics can
be used to measure the dimensions of reality, but not to verify the
moments of reality.
Let me introduce you to Dick Adams' Three Laws of Statistical
Analysis (from my unpublished paper "The Statistical Demise of 
the Moss Klein Pitcher):
First Law:   Every non-uniform distribution can be expected to
             have a tail.
Second Law:  Fairy tales come true in the tails of a distribution.
Third Law:   Anyone who proposes an argument based on the tails
             of a distribution without rigorous proof of a link
             to reality should expect their argument to be viewed
             as being without merit and is deserving of the 
             ridicule received.
When I apply Occam's Razor, Dr. Sagan's presentation is superior
to mine.  But then he was being scientific while I was being
sarcastic.
Life elsewhere in the universe is probable; finding it may well
be the greatest discovery ever made up to that time.
Dick -- There are no Statisticians.  We are all just students of
        Statistics striving to learn more each day.

On Mon, 20 Jan 1997 16:22:59, wpenrose@interaccess.com (William R.
Penrose) wrote:
>In article <5bsc70$f1d@csu-b.csuohio.edu> drake.79@osu.edu (Macarthur Drake) writes:
>
>>This messege is to provoke a serious scientific debate.
>
>                      
>>                        Logical and insightfully comments welcomed!
>
>Sure, here's a comment:  Next time, don't spam every newsgroup in the known 
>universe with your deathless observations.
>
>Bill
>
>
    What if they decide that we are delicious?
 Boris Mohar

Hi, can anyone provide me with a reference for calculating standard
errors for indirect effects in path analysis models? I have exhausted
all resources available to me without success.
Any help will be greatly appreciated.
Andrew.

My employer wants to know if the test results from two instruments that
measure the same physical property are "the same".  I think this is
called reproducability (sp?).  In each of the few books I have
available, there is always at least one term in the example equations
that I don't understand.  I understand averaging, standard deviation and
can calculate simple regression.  Although I must admit I don't
understand all the regression terms Lotus123 returns, after slope,
offset and R ^2 I'm lost.  Is there a "simple" set of equations that one
uses for this type of study, or could someone recommend a text/source I
should look at.  Please excuse my barging in here for help.  I've not
read your group before and hate to presume that I can just ask and
recieve, but my boss is somewhat "in a hurry" ;-).  Thanks so much for
your time, John.

Macarthur Drake wrote:
> 
> This messege is to provoke a serious scientific debate.
> 
>         I am an engineer, no biologist, astronomer or statictician or
> anything, but something puzzles me. I am sure you are aware of the Late Dr.
> Sagan's quote  " extraordinary claims require extraordinary proof " with
> regards to extraterrestrial life, UFOs etc. I have also heard people say
> that the discovery of life on another world would be the greatest discovery
> in human history.
>          I beg to differ with both of these ridiculus statments. From my
> understanding of biochemistry and the number of stars in the universe....to
> not find life would be the greatest discovery of all times. There is nothing
snip
>         I would appriciate any math or stats expert to comment on the
> chances that we are alone in the entire universe. I bet that s/he'd say that
> it is statistically impossible for us to be alone, so what's the big deal we
> know that life is there, just a matter of time 'til we find it....or them
> us!
>         By the way there are an estimated 100 million million million stars
> or as Dr. Sagan put it more stars than the number of grains of sand on all
> the beaches/deserts on the entire Earth!
> 
>                         Logical and insightfully comments welcomed!
> 
>         drake.79@osu.edu
Experts in math and stats could provide no meaningful incite unless they
were also expert in Biochemistry.  More expert, in fact, than anyone
currently is. Statistics does not provide one with a magical elixir to
make meaningful predictions from a point of ignorance.  As far as my
biological knowledge goes, this is the bare essentials for life:
liquid water
20 amino acids (and their biosynthetic pathways, unless the primordial
soup is extremely rich)
20 tRNA'a
20 tRNA synthetases
functional ribosomes
An RNA-dependent RNA-polymerase (I skip DNA to make it easier)
RNA which codes for the last 4 requirements
Note that all of these must be present simultaneously.  RNA that codes
for ribosomes will do no good unless their is already a ribosome to
implement it.  RNA polymerase will do no good unless there is already
RNA (coding for the polymerase) to duplicate, and etc.
To be more generous, let's say we only need 5 amino acids, tRNA's, and
synthetases.  Still looks pretty darn unlikely, even for billions of
stars and billions of years.
Of course life doesn't have to start this complicated.  It could have
consisted only of catalyic RNA at first.  But we have little to no
evidence that RNA can catalyze such a range of transformations.
Until (or unless) we learn more about the beginnings of life on this
planet, we cannot even speculate to within a power of 10, or for that
matter a power of 1000000000, the likelihood of life elsewhere.
Jeff

As I see it, there is one big problem with the whole debate.  The most
likely number of stars in the universe that have life is equal to the
product of the number of stars and the probability that any one star had
the right conditions to foster the formation of life.  We know the number
of stars, roughly speaking.  If the probability of life forming around any
one of these stars is much less than 1/(the number of stars), then the
product is small and it is unlikely that there is other life out there.  On
the other hand, if the probability that any one star has the right
conditions to give rise to life is of the order  of 1/(the number of stars)
or greater, then there is a great likelihood that some other star has life
circling it.
The problem is that we have *absolutely* no way to rationally assess the
probability that any given star has the right conditions to have given rise
to life or intelligent life.  All we have is the two emotional "arguments",
a)  "There are *so* many stars, there *must* be other intelligent life out
there." 
and 
b) "The formation of life is *so* improbable that it *can't* have happened
more than once in the universe."  
Unfortunately, both of these arguments have exactly equal validity and
probability until we have some means of assessing how probable (or
improbable) the origin of intelligent life at any spot in the universe
might have been.
	Eric Lucas
Macarthur Drake  wrote in article
<5bsc70$f1d@csu-b.csuohio.edu>...
> This messege is to provoke a serious scientific debate.
> 
> 	I am an engineer, no biologist, astronomer or statictician or 
> anything, but something puzzles me. I am sure you are aware of the Late
Dr. 
> Sagan's quote  " extraordinary claims require extraordinary proof " with 
> regards to extraterrestrial life, UFOs etc. I have also heard people say 
> that the discovery of life on another world would be the greatest
discovery 
> in human history.
> 	 I beg to differ with both of these ridiculus statments. From my 
> understanding of biochemistry and the number of stars in the
universe....to 
> not find life would be the greatest discovery of all times. There is
nothing 
> extraordinary about looking the biochemistry of life and looking at the 
> billions of stars (in this galaxy alone) and concluding that there MUST
be 
> life out there. From a scientific view, there is nothing unique about
amino 
> acids.....the elements that make them up are not located only on this
planet 
> for sure. Now if there were only 10 stars in the entire universe the Dr. 
> Sagan's stament maybe more logical. But we can say, based upon all our 
> scientific theories, that LIFE MUST  exist elsewhare in the universe. If 
> not, then everything we understand about the universe is false. I even 
> suspect that life is rather common, say every 20,000 stars or so.
> 	Now I am not saying that UFO are here or anything, just that life 
> must exist. Maybe they are just prokaryots or something, but that is
life. 
> Why all the hype? We know that alien life MUST exist in some form or 
> another, so why get so excited? Now the debate over UFOs and aliens
visiting 
> is another story, although I think that can be debated scientifically
also. 
> I'd be glad to do that with anyone who likes debating as much as I do.
> 	I would appriciate any math or stats expert to comment on the 
> chances that we are alone in the entire universe. I bet that s/he'd say
that 
> it is statistically impossible for us to be alone, so what's the big deal
we 
> know that life is there, just a matter of time 'til we find it....or them
> us!
> 	By the way there are an estimated 100 million million million stars 
> or as Dr. Sagan put it more stars than the number of grains of sand on
all 
> the beaches/deserts on the entire Earth!
> 			
> 			Logical and insightfully comments welcomed!
> 
> 
> 
> 	drake.79@osu.edu
> 
> 
> 

Roger Balakrishnan wrote:
> 
> hi,
> 
> I have the following question on my statistics
> assignment and Im not sure how to go about
> solving it :
> 
> S^2 is the variance of a random sample of size
> n from a N(mu,sigma^2) population.
> Prove that
> 
>  g = n S^2/ (n-1) converges in probability to
> 
>      sigma^2.
> 
> Im not sure how to go about solving this problem.
> I know  nS^2/sigma^2 ~ Chi-squared (n-1), using
> this and the approp. transformation I can get
> the density function for g. Is this the right
> approach or am I missing something.
> 
> thanks,
> 
> roger
g is sigma^2/(n-1) times a variable T that is chi-square on n-1
degrees of freedom. Write g = (sigma^2/(n-1))*T.
Then E(g) = (sigma^2/(n-1))E(T) = sigma^2.
Var(g) = (sigma^4/(n-1)^2)*var(T) = (sigma^4/(n-1)^2)*2*(n-1)=
2*sigma^4/(n-1) which approaches zero so you can use 
Chebyshev's inequality.
Ellen
Now you can use Chebyshev's inequality:
Pr(abs(g-E(g)) >= d) <= Var(g)/d^2 which approaches zero.

Macarthur Drake wrote:
>         Also very cute, but I thought I missed
> 'alt.correct.my.english.please'...if not then I'll do so next time. Remember
> it is the thought that counts....words are just a specific pattern of
> varying density of air...and typed words on computers are just a bunch on
> transmitted electrons...so lighten up buddy....
"Lighten up" from someone who said "I beg to differ with both of these
ridiculus statments."  Go figure.
-- 
D.
mentock@mindSpring.com
http://www.mindspring.com/~mentock/index.htm

Roger Balakrishnan   wrote in article <5c0gtt$9g9@bmerhc5e.bnr.ca>...
| 
| hi,
| 
| I have the following question on my statistics 
| assignment and Im not sure how to go about 
| solving it :
| 
| S^2 is the variance of a random sample of size 
| n from a N(mu,sigma^2) population.
| Prove that 
| 
|  g = n S^2/ (n-1) converges in probability to 
| 
|      sigma^2.
| 
| 
| Im not sure how to go about solving this problem.
| I know  nS^2/sigma^2 ~ Chi-squared (n-1), using
| this and the approp. transformation I can get 
| the density function for g. Is this the right 
| approach or am I missing something.
First, write out what it means for g to converge in probability to sig^2.
Second, re-arrange the inequality expression, whose probability is under
cosideration, to get a difference between nS^2/sig^2 and its expectation.
Third, apply the Chebyshev inequality. 
Fourth, consider the limit as n->oo.
(So you need to find both the expectation and the variance of nS^2/sig^2.)

>>                        Logical and insightfully comments welcomed!
>
>Sure, here's a comment:  Next time, don't spam every newsgroup in the known 
>universe with your deathless observations.
>
>Bill
>
	Cute, but the reason why I did post to so many is because it touches 
on several aspects of science. For example, a biologist that has studied 
ancient life may be able to comment on the beginings of life.

In article <5c0t8g$j5g@access1.digex.net>, rdadams@access1.digex.net says...
>
>Macarthur Drake  wrote:
>> This messege is to provoke a serious scientific debate.
>
>Then it should have been written more seriously and without
>a plethora of spelling and grammatical errors!!
>
	Also very cute, but I thought I missed 
'alt.correct.my.english.please'...if not then I'll do so next time. Remember 
it is the thought that counts....words are just a specific pattern of 
varying density of air...and typed words on computers are just a bunch on 
transmitted electrons...so lighten up buddy....

I need a (working) algorithm which would give me a cluster size
distribution for a Probabilistic Cellular Automaton.
My system: a matrix containing 0's and 1's.
Cluster: a set of 1's connected by nearest neighbours (4 on a square
lattice).
Wanted: a matrix containing cluster number (1,2,...) instead of 1's in
the initial matrix.
I've tried to implement the Hoshen-Kopelman Method, but failed as yet. I
prefer a standard-C code if possible, but any suggestion will be greatly
appreciated (acknowledged in a paper !).
My e-mail address:      ak133@cus.cam.ac.uk
or:                     adam@zoo.cam.ac.uk
Thanks in advance,
Adam Kleczkowski
-- 
Adam Kleczkowski, King's College and Dept. of Plant Sciences
Univ. of Cambridge, Downing Street, Cambridge CB2 3EA, England
tel. (+44)(1223)330229, fax  (+44)(1223)333953,
e-mail ak133@cus.cam.ac.uk, WWW http://www-epidem.plantsci.cam.ac.uk

In <5c1kqi$cdj@csu-b.csuohio.edu> drake.79@osu.edu (Macarthur Drake)
writes: 
>
>In article <5c0t8g$j5g@access1.digex.net>, rdadams@access1.digex.net
says...
>>
>>Macarthur Drake  wrote:
>>> This messege is to provoke a serious scientific debate.
>>
>>Then it should have been written more seriously and without
>>a plethora of spelling and grammatical errors!!
>>
>
>
>	Also very cute, but I thought I missed 
>'alt.correct.my.english.please'...if not then I'll do so next time.
Remember 
>it is the thought that counts....words are just a specific pattern of 
>varying density of air...and typed words on computers are just a bunch
on 
>transmitted electrons...so lighten up buddy....
>
I'm interested in knowing about the star of CANOPUS? What the name
means, it's history, how far away it is, it's size, it's spectral
class, can NASA ever send a spaceship there, what constellation it's
in. Any information would be greatly appreciated.
COHEN
america2@ix.netcom.com

The probability of life elsewhere other than planet earth is exactly
1.0! This is a true statement and I have evidence! So does NASA in so
far as they keep blasting it into space. Suffice it to say that there
is life in space at this very moment. Moreover, what goes up must come
down!
It's all relative, but there still ain't no absolutes. If in theory
one wanted to assert that 'life must exist on another planet' one
would also have to assert that life did not exist on another planet
if one was to make these assertions within frames of
empiricism/science. To assert that 'alien life' existed one would need
empirical evidence to back the assertion and no one has
any. Theoretically, if one says that 'alien life' does indeed exist,
but they have no empirical proof to back the assertion, it is not
theory but more aptly dogmatic posturing.
-- 
   ----------------------------------------- Carleton University ----------
               Robert G. White               Dept. of Psychology   
                                             Ottawa, Ontario. CANADA
   INTERNET ADDRESS ----- rwhite@ccs.carleton.ca ------------------- E-MAIL
   ------------------------------------------------------------------------

William R. Penrose  wrote in article
...
> In article <5bsc70$f1d@csu-b.csuohio.edu> drake.79@osu.edu (Macarthur
Drake) writes:
> 
> The first man on the moon was supposed to be the event of the century. 
While 
> exciting at the time, its net effect on my life has been a lot less than
my 
> dog throwing up on the living room rug, my grand-daughter's birthday, or
even 
> the OJ trial.  Same goes for "life" on Mars.
> 
Oh, I gotta disagree.  Although this also brings up arguments about space
spin-off's, I think everyone understands Transistors, IC's, satcomm, and
other space technologies as being useful.
Nobody thought Columbus was very smart either.  Aren't you glad he tried?
Some people look forward, most people look at their shoes.
		== John ==

John Coffman wrote:
> 
> My employer wants to know if the test results from two instruments that
> measure the same physical property are "the same".  I think this is
> called reproducability (sp?).  In each of the few books I have
> available, there is always at least one term in the example equations
> that I don't understand.  I understand averaging, standard deviation and
> can calculate simple regression.  Although I must admit I don't
> understand all the regression terms Lotus123 returns, after slope,
> offset and R ^2 I'm lost.  Is there a "simple" set of equations that one
> uses for this type of study, or could someone recommend a text/source I
> should look at.  Please excuse my barging in here for help.  I've not
> read your group before and hate to presume that I can just ask and
> recieve, but my boss is somewhat "in a hurry" ;-).  Thanks so much for
> your time, John.
To my knowledge it is impossible to show, that two test results are "the
same". One can only show, that they do not differ by more than a given
difference. This difference must be set in advance together with an
adequate design of the experiments.
If the decision about the two instruments is of importance, then you or
your company should seek the advice of an experienced statistician !
Peter Dittrich

In article <5c21vj$30v@dfw-ixnews12.ix.netcom.com> america2@ix.netcom.com (Brad) writes:
>In <5c1kqi$cdj@csu-b.csuohio.edu> drake.79@osu.edu (Macarthur Drake)
>writes: 
>>
>>In article <5c0t8g$j5g@access1.digex.net>, rdadams@access1.digex.net
>says...
>>>
>>>Macarthur Drake  wrote:
>>>> This messege is to provoke a serious scientific debate.
>>>
>>>Then it should have been written more seriously and without
>>>a plethora of spelling and grammatical errors!!
>>>
>>
>>
>>	Also very cute, but I thought I missed 
>>'alt.correct.my.english.please'...if not then I'll do so next time.
>Remember 
>>it is the thought that counts....words are just a specific pattern of 
>>varying density of air...and typed words on computers are just a bunch
>on 
>>transmitted electrons...so lighten up buddy....
>>
>
>I'm interested in knowing about the star of CANOPUS? What the name
>means, it's history, how far away it is, it's size, it's spectral
>class, can NASA ever send a spaceship there, what constellation it's
>in. Any information would be greatly appreciated.
>
>COHEN
>
>america2@ix.netcom.com
>
Canopus:  Apparent visual magnitude -0.72, second brightest star in the
sky after Sirius, also called alpha Carinae (Carina = keel).  Carina was
part of the great constellation Argo Navis, ship of the argonauts, which
was subdivided in the 1750s into deck(Puppis), keel(Carina) and sails
(Vela).  Named for the pilot of King Menelaus' fleet of ships.  Spectral
class A9 II, so it is essentially a supergiant (some references may give
F0 Ib).  Distance about 1200 light years.  It is unlikely that NASA or
anyone else will ever send a spaceship there! Not soon, anyways. 
Can not be seen from north of approximately latitude 38 degrees.
-- 
Mike Dworetsky, Department of Physics  | Bismarck's law: The less people
& Astronomy, University College London | know about how sausages and laws
Gower Street, London WC1E 6BT  UK      | are made, the better they'll
   email: mmd@star.ucl.ac.uk           | sleep at night.

drake.79@osu.edu (Macarthur Drake) writes: 
> rdadams@access1.digex.net says...
>> Macarthur Drake  wrote:
>>> This messege is to provoke a serious scientific debate.
>> Then it should have been written more seriously and without
>> a plethora of spelling and grammatical errors!!
>	Also very cute, but I thought I missed 
> 'alt.correct.my.english.please'...if not then I'll do so next time.
Considering how many newsgroups you spammed, I'm surprised you
missed that one.
> Remember it is the thought that counts .... words are just a specific
> pattern of varying density of air...and typed words on computers are
> just a bunch on transmitted electrons...so lighten up buddy....
Something tells me that argument "ain't gonna make it" when you turn
in the first draft of your dissertation.  
As for "serious scientific debate", it's noteworthy that you responded
to the last phrase of my first sentence and completely ignored the
structural content of my response.
Dick

"\"Uncle Al\" Schwartz" <#UncleAl0@ix.netcom.com> wrote:
> The basic chemistry of star tar is default carbon-based life.  Start
> with a large plop which, for whatever reason, contains liquid water and
> you are in business.  Look at what infests Antarctic sandstone, deep sea
> ridges, and wet basalt two miles underground.  The Miller and
> Ponamperuma experiments generate abiotic fatty acids, sugars, amino
> acids, nucleic acid bases... and ordered coacervate droplets within a
> week.  Give it a billion years to organize in a diversity of physical
> and chemical environments.
> 
> The problem is that billion years.  The Earth is unique in that 2/3 of
> its planetary crust is orbiting 240,000 miles overhead - the Moon.
> 
Rare perhaps, but almost certainly not unique. Presumably the event
(collision?) that put so much of earth's crust into orbit could happen
elsewhere, and at any rate there could be other possible scenarios that
might bring all the right materials together under the conditions needed
for life to evolve and remain undisturbed enough to where civilization
could develope.
Frank

John D. Gwinner wrote:
> 
> William R. Penrose  wrote in article
> ...
> > In article <5bsc70$f1d@csu-b.csuohio.edu> drake.79@osu.edu (Macarthur
> Drake) writes:
> >
> 
> > The first man on the moon was supposed to be the event of the century.
> While
> > exciting at the time, its net effect on my life has been a lot less than
> my
> > dog throwing up on the living room rug, my grand-daughter's birthday, or
> even
> > the OJ trial.  Same goes for "life" on Mars.
> >
> 
> Oh, I gotta disagree.  Although this also brings up arguments about space
> spin-off's, I think everyone understands Transistors, IC's, satcomm, and
> other space technologies as being useful.
> 
> Nobody thought Columbus was very smart either.  Aren't you glad he tried?
>
This is a very interesting question.   Columbus differed with the more
knowledgeable geographers and navigational scientists of his time about
the size of Asia and/or the circumference of the Earth.  He was wrong,
and they were right, but he was lucky that there was a previously
unknown (except to the Vikings) continent between Europe and Asia to
the east.   One can conjecture about what would have happened had
he failed.   It is fairly clear that eventually Europeans would
have found the `New World', which I remind you had already been found
many thousands of years earlier by other members of our species.  (There
were even at least three highly developed civilizations on the North and
South American continents.)  Probably the most significant barrier to
such voyages of discovery was the inability to determine longitude. 
This was solved by a combination of astronomical techniques and the
development of highly accurate clocks.   It seems likely that by the
eighteenth century Eruopeans would have made the same discovery if not
earlier.  But the Inca, Mayan, and other societies might have developed
further in the interim, and it is not clear what the result would have
been.   I suspect that many Europeans would have migrated to the
Americas but it might have been under very different circumstances.  The
institution of African slavery might not have become established in the
Western hemisphere.   Someone could easily write an alternate history of
such a world, and perhaps it has been done.   Since many of us wouldn't
be alive in the alternate world, the majority of us might not approve,
but it is not clear it wouldn't be just as good (or bad) a world as the
one we have.
> Some people look forward, most people look at their shoes.
> 
>                 == John ==
-- 
Leonard Evens       len@math.nwu.edu      491-5537
Department of Mathematics, Norwthwestern University
Evanston Illinois

A good reference that is not too statistical is "Concepts for R&R; Studies"
 by Larry Barrentine.  you can buy a copy from ASQC press.
A better way to address that type of problem, however is to perform an
Analysis of Variance to determine if any extra variation in test results
can be attributed to the instruments.  This is also a useful method of
determining any difference between operators.  
If you have a statistical reference, read up on ANOVA.
Craig Bernier

Macarthur Drake wrote:
>         I am an engineer, no biologist, astronomer or statictician or
> anything, but something puzzles me. I am sure you are aware of the Late
> Dr.
> Sagan's quote  " extraordinary claims require extraordinary proof " with
> regards to extraterrestrial life, UFOs etc.
Specifically, he was talking about UFOs being aliens spacecraft.  It's not
the claim that extraterrestrial life exists that Sagan was calling an
extraordinary claim, it's that the aliens were regularly visiting Earth
surrpetitiously (but very poorly since they always seem to be seen).
> But we can say, based upon all our
> scientific theories, that LIFE MUST  exist elsewhare in the universe. If
> not, then everything we understand about the universe is false.
Yes.  The question is not whether or life is possible or not, but how
common it is -- and, furthermore, how common _intelligent_ life is.  For
that science has no answers.
Besides, don't knock confirming theories, even the ones that we're sure
about.  That's how science works.
-- 
        Erik Max Francis, &tSftDotIotE; / email:  max@alcyone.com
                      Alcyone Systems /   web:  http://www.alcyone.com/max/
 San Jose, California, United States /  icbm:  37 20 07 N  121 53 38 W
                                    \
           "Gods are born and die, / but the atom endures."
                                  / (Alexander Chase)

In article  orourke@utstat.toronto.edu (Keith O'Rourke) writes:
>You may wish to look at the capter called something like
>"Hunting out the real uncertainty" 
>
>in
>
>Mosteller & Tukey *something* Regressiona Analysis *something* 
>197*something*
Data Analysis and Regression: a second course in statistics
Addison-Wesley, 1977
IMHO a GREAT book
Peter

s1097716@aix2.uottawa.ca (Tim Creasy) wrote:
>If X and Y are independent and have identical Gaussian distributions N(0,sigma)
>what is the distribution of Z = X*Y?  Or at least its variance?
>
>Solutions or references on this would be much appreciated.
>
if x is normal(0,sigmax) and y is normal(0,sigmay)
then if z=xy
p(z) = K0(|z|/(sigmax*sigmay))/(pi*sigmax*sigmay)
where K0 is the zero order Bessel function of the second kind.
This result from W.S.Burdic: "Underwater Acoustic system Analysis", 
Prentice Hall.
Derivation is in any good statistics text book, eg. M.G.Kendall: 
"Advanced theory of Statistics".
JEH

Bill Sampson (sampson@sun.ps.umist.ac.uk) wrote:
: Is the sum of gamma distributions, with different
: means and variances, itself a gamma distributed 
: variable? I expected this to be so, and calculated
: the pdf and associated mean and variance of the
: resulting distribution. The pdf looks lognormal -
: however, a plot of the new pdf along with that of
: a gamma distribution of the same mean and variance 
: shows them to be similar - but not the same. 
: So, is the sum of gammas gamma, or is it just well
: approximated by a gamma?
Let alpha be the shape parameter and beta be the scale parameter.  Then
the mean is alpha*beta and the variance is alpha*beta^2.  If two gammas
have the SAME scale parameter beta and shape parameters alpha_1 and
alpha_2, then their sum is gamma with shape parameter alpha_1 + alpha_2
and scale parameter beta.  This can be seen by looking at the
characteristic functions or directly computing the convolutions.  If the
scale parameters are different, it is fairly easy to see the sum cannot be
gamma. 
-- 
Michael P. Cohen                       home phone   202-232-4651
1615 Q Street NW #T-1                  office phone 202-219-1917
Washington, DC 20009-6310              office fax   202-219-2061
mcohen@cpcug.org

In article <32E41634.2178@uclink4.berkeley.edu>, jejanes@uclink4.berkeley.edu wrote:
> Experts in math and stats could provide no meaningful incite unless they
> were also expert in Biochemistry.  More expert, in fact, than anyone
> currently is. Statistics does not provide one with a magical elixir to
> make meaningful predictions from a point of ignorance.  As far as my
> biological knowledge goes, this is the bare essentials for life:
> 
> liquid water
> 20 amino acids (and their biosynthetic pathways, unless the primordial
> soup is extremely rich)
> 
> 20 tRNA'a
> 20 tRNA synthetases
> functional ribosomes
> An RNA-dependent RNA-polymerase (I skip DNA to make it easier)
> RNA which codes for the last 4 requirements
> 
Add a pinch of salt, bake at 350 degrees for 2 hours and voila
    ... Pauley Shore.

>From: bm373592@muenchen.org (Uenal Mutlu)
>
>We have to seperate the things:
>
> - probability of 54 fixed  tickets in  1 drawing
> - probability of  1 fixed  ticket  in 54 drawings
> - probability of 54 fixed  tickets in 54 drawings
>
> - probability of 54 random tickets in  1 drawing
> - probability of  1 random ticket  in 54 drawings
> - probability of 54 random tickets in 54 drawings
>
>(there are no duplicate tickets in each case)
>
>Can someone calculate some or all of them?
We have already shown you that 1 ticket in 54 draws has about 63%
chance of winning.  It's totally irrelevant how it's selected.
By the same token, when you say 'random' above you mean that the
set of tickets was SELECTED randomly.  Because of this, you can
expect a variation in the percent of coverage.  Like I stated before,
in the case of 27 tickets in 1 draw, you can expect the percentage to
vary from 4.7% to about 45%.  So for 54 tickets it would be in the
range of 15% to 75%.  So the probability for the 54 drawings will
also be a range.
What you have to understand is that the EXACT probability of a set of
tickets can only be calculated AFTER it is selected.  And once it IS
selected, then it's a FIXED set!!  A random set of tickets cannot have
an EXACT probability, only a range.

John D. Gwinner wrote:
> 
> William R. Penrose  wrote in article
> ...
> Nobody thought Columbus was very smart either.  Aren't you glad he tried?
Do you really want us to answer that?
Pete.

         COMPUTER PROGRAMMER II: Section of Computer Science,
                    Department of Biomathematics,
         The University of Texas M. D. Anderson Cancer Center
                             Houston, TX
OVERVIEW: Our group  develops   computer code to provide   statistical
capabilities needed in cancer research but not available commercially.
The  code  so developed is  posted   for  general  use.  We also  test
competing  methods  for  performing common  statistical  functions and
report on the comparisons.  Examples of comparisons include methods to
correct  for multiple testing and  methods for confidence intervals in
binomial proportions.
REQUIREMENTS:  College  degree (M.S.   preferred) in  a science and at
least   one year  of relevant  experience.    A good  understanding of
statistical philosophy and methods is necessary to understand tasks to
be performed.  We strive  for quality, hence knowledge and application
of good coding   practices are required.   A high  level  of oral  and
written communications ability is necessary to refine computer program
specifications  and  to internally and externally    document code.  A
general knowledge of numeric methods is a definite plus.
JOB DESCRIPTION: The programmer will receive general, sometimes vague,
specifications from  a  faculty member.  The  programmer considers and
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The programmer designs code  through successive refinement,  a process
that may well involve further discussions.  The programmer writes code
and  drafts  documentation.  As all    software developers know,  this
process may well be iterated.
ENVIRONMENT:  The primary compute servers  are  Unix machines with the
usual utilities  (e.g.,   EMACS,  LaTeX).   Our   standard  procedural
language is Fortran 77;  we are considering  switching to  Fortran 90.
We also write a  good  deal of code in  Splus.   We have most of   the
standard scientific software (Maple, Mathematica,  SAS, etc.) as  well
as language translators: Fortran to C, f77 to f90.
NOTE:   The successful applicant need  not  know Fortran or Splus, but
will be expected to rapidly learn them.  Our  experience has been that
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MORE  INFORMATION: on the Section, Department,  and Institution can be
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                      http://odin.mdacc.tmc.edu/
SALARY RANGE: For a holder of a B.S. and one year's experience, the
salary is somewhat less than $30K.  With a M.S. and several years
experience the salary could be $40K or slightly more.  
IF INTERESTED: contact Barry W. Brown.
                                       Barry W. Brown
                                       Department of Biomathematics, 
                                            Box 237
                                       University of Texas M. D.
                                            Anderson Cancer Center
                                       1515 Holcombe Blvd
                                       Houston, TX 77030
NEW EMAIL ADDRESS
bwb@odin.mdacc.tmc.edu
internet address is (143.111.62.32)

Let X and Y denote zero mean, unit variance Gaussian 
variables, with r = average(X*Y).  If Z = X*Y then
the probability density function of Z is 
PDF(Z) =       1
         --------------   exp(r*Z/sqrt(1-r^2) ) K0(Z/sqrt(1-r^2) )
          PI * sqrt(1-r^2)
This is bad news, because K0 is among the less tractable Bessel 
functions.  I have not been able to find a published reference 
which gives this formula.
>From: s1097716@aix2.uottawa.ca (Tim Creasy)
>Newsgroups: sci.stat.math
>Subject: Distribution of product of Gaussians?
>Date: 18 Jan 1997 21:49:59 GMT
>Organization: University of Ottawa
>
>If X and Y are independent and have identical Gaussian distributions N(0,sigma)
>what is the distribution of Z = X*Y?  Or at least its variance?
>Tim
----------------------------------------------------------------------------
I speak only for myself.  For all I know, there may be someone in some
organization who agrees with me.  But I have no idea who or where.

Hello Everyone.
Does anyone know of a procedure that can calculate the optimal
combination of variables based on the value of an independent
variable?  I have a matrix of 13 BY 13 variables.  From that
matrix, I would like to know what combination produces the
highest average from an independent variable.
I guess this would be a probability matrix of 13! [factorial].
Any help would be appreciated.

Is it possible???
   Base - theory of  Teilhard de Shardin.
 Creation of Hyper brain:
Increasing speed of net ~ 10000 times.
Direct contact  from net to brain , virtual reality(?).
Self-organization of initial seed - new evolution structure.
Finally, new structure restricted only geometrically, by surface       
of planet and by  number  of involved  humans (sells of Hyper brain).
Power of Hyper Brain  will excel power of human brain,
as human brain excel power of  brain cell.
Power of Hyper Brain is INFINITE. 
Evolution  approaches to omega point - crown of evolution on
earth and , finally, in universe.
Earth  is unique place in universe - if  this
process  was going somewhere else ,Omega would involve us
already.
     ================================================
      WE ALONE IN UNIVERSE, BECAUSE WE ARE FIRST !??
     ================================================
It puzzle me long time, please, any comment.
Thank you.
Val.

Dear Mathematicians,
Let P be the transition matrix of an ergodic, finite Markov
chain.  P has elements p(j, k).  With each transition (j, k),
associate a moment generating function f(j,k,t).  A random
variable X_i is defined on this chain such that X_i has
the distribution associated with f(j, k, t) if the i-th
transition of the chain is from state j to state k.
Form a new matrix P(t), where the elements are p(j, k)f(j, k, t).
Let m(t) be the maximal positive eigenvalue of P(t).
Given those definitions, the result I'm trying to understand is:
If the chain is started with the initial state distributed
according to the ergodic distribution associated with P, and
if we take expectation unconditional on the next state,
"it is easy to show that E(X_1) = m'(0)."  (m'(.) is the
derivative with respect to t of the maximal eigenvalue.)
The reference for the paper making this claim is:
H.D. Miller, "A convexity property in the theory of random variables
defined on a finite Markov chain," Ann. Math. Stat., v32, pp. 1260-1270
1961.
The claim appears on the second page of the paper.
Your insight will be greatly appreciated.  Thank you for your time.
Doug Obal

RF Drost wrote:
> 
> In article <32E41634.2178@uclink4.berkeley.edu>, jejanes@uclink4.berkeley.edu wrote:
> 
> > Experts in math and stats could provide no meaningful incite unless they
> > were also expert in Biochemistry.  More expert, in fact, than anyone
> > currently is. Statistics does not provide one with a magical elixir to
> > make meaningful predictions from a point of ignorance.  As far as my
> > biological knowledge goes, this is the bare essentials for life:
> >
> > liquid water
> > 20 amino acids (and their biosynthetic pathways, unless the primordial
> > soup is extremely rich)
> >
> > 20 tRNA'a
> > 20 tRNA synthetases
> > functional ribosomes
> > An RNA-dependent RNA-polymerase (I skip DNA to make it easier)
> > RNA which codes for the last 4 requirements
> >
> 
> Add a pinch of salt, bake at 350 degrees for 2 hours and voila
>     ... Pauley Shore.
Damn! And there I was, thinking "sugar and spice and everything nice"
and "frogs and snails and puppy dog tails"!
Ramsa