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Re: [Phys-L] From a Math Prof (physics BS major) at my institution ( math cha

I was so shocked that I had someone take a picture to commemorate the event.

<http://www.google.com/imgres?imgrefurl=http%3A%2F%2Fwww.dogsplayingpoker.org%2Fgallery%2Fcoolidge%2F&tbnid=Bc-AQaRLmMW4AM:&docid=4Ls_nE3m-FRrlM&h=540&w=800>

:-)

Bob at PC

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Anthony
Lapinski
Sent: Tuesday, February 18, 2014 11:21 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my institution (
math cha

Random, of course (assuming the cards were properly shuffled, etc.).

More importantly, did you win the hand?



Phys-L@Phys-L.org writes:
I was playing poker last night and was dealt a hand that was 5-6-7-8-9
all hearts. Was that random - or did the dealer fix the hand?

There is no test that can truly tell the randomness of the two lists
with so few numbers.

Bob at PC

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Rauber,
Joel
Sent: Tuesday, February 18, 2014 10:47 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution (
math challenge)

The second list was the random list. As noted, one cannot prove
which
one
was the random list, you can only make a probabilistic guess.

I looked at two factors, the number of times consecutive numbers
appear
->
leads to 2nd list is random The number of times numbers in the range
[30-35]
appeared compared to the other decade ranges, which also lends
evidence that the second list was the random one.

I didn't personally calculate it, but the Math Prof. told me that the
probability
of consecutive numbers appearing on a truly random list is 48%, much
higher
than most people would guess.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Jeffrey
Schnick
Sent: Monday, February 17, 2014 8:49 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution (
math challenge)

Only two of the numbers in the first list end in 0. Thus, I think
the
first list
was made up by people.
________________________________________
From: Phys-l [phys-l-bounces@phys-l.org] on behalf of Philip Keller
[pkeller@holmdelschools.org]
Sent: Monday, February 17, 2014 6:59 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)

I am going the other way here. I think the students would feel the
need to
choose a wide range of numbers. But I calculate that in 21 sets like
this, we
would expect just under 5 of the sets to have no single-digit numbers.
The
first batch has 2 like that, and the second has 6. So I pick the
second batch as
real, 1st batch as student-generated.


On 2/17/2014 4:04 PM, Donald Polvani wrote:
Not being familiar with random number tests, I had to take a simple
(and
crude) test. If the numbers are truly random and have been
arranged in numerical order, then the first column would be
expected the have numbers from 1 - 7, with successive columns
having numbers between 8 - 14, 15 - 21,
22 - 28, and 29 - 35.

So a very simple test is to simply count the number of times that
numbers in each column exceed (or fall below) the expected column
limits. For the first set of numbers, I find that the column
limits were exceeded, respectively, 5, 8, 6, 4, and 5 times (for
the last column I counted the number of times the listed number
fell below the lower column limit). Doing this for the second set
of numbers produced the excess numbers 8, 11, 10, 4, and 7 (again,
for the last column I counted the number of times the listed number
fell below the
lower column limit).

Clearly the second set of numbers failed the column limit tests
more often and should be (i.e. "probably is") the student list.

Don

Dr. Donald Polvani
Anne Arundel Community College
Adjunct Faculty, Physics (Retired)
Arnold, MD

--Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of
Rauber, Joel
Sent: Monday, February 17, 2014 2:08 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)

Before giving it away, both lists are in numerical order smallest
to largest; so that has been ordered after the numbers were generated.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of
Jeffrey Schnick
Sent: Monday, February 17, 2014 11:32 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)

Each set of five numbers in the first set is listed in numerical
order from smallest to largest. Thus, I think the first group was
student
generated.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Paul
Nord
Sent: Monday, February 17, 2014 12:28 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)

That's easy.

The first group is the real lottery numbers. It is more uniformly
distributed.
In the second set, the student-generated numbers, numbers in the
20's are much preferred.

Paul


On Feb 17, 2014, at 10:33 AM, Rauber, Joel
<Joel.Rauber@SDSTATE.EDU>
wrote:

The below may be tangentially related to discussions of entropy
(See subject heading)


I asked my Math 316 (Discrete Math) to randomly pick 5 numbers
from
1 to
35. This is the same as the "South Dakota Cash Lottery" that has
drawings twice a week. I told them that I would compare their
"random" numbers to actual numbers drawn in the lottery. They
were instructed to try to make their numbers as random as possible
so they looked just like the real random numbers. I had 21
responses, they are in one of the two lists below. The other list
is the numbers drawn in the lottery from Dec 7, 2013 to Feb 15,
2014. Can you tell which list is the student's list? Hint: there
is an easy, almost trivial,
way to do this, or least to locate the most likely student list.

02-06-07-25-34
03-09-12-15-34
06-16-21-28-32
06-10-13-21-23
04-18-26-27-34
03-06-17-27-32
03-11-21-22-35
01-02-08-17-27
07-12-14-24-31
03-07-14-18-27
07-13-22-25-31
07-12-23-31-32
04-17-18-22-35
08-15-17-20-25
12-16-18-29-34
02-07-11-16-21
08-23-24-32-35
17-19-23-29-31
09-16-27-28-32
06-15-19-26-32
06-13-15-23-31



11-17-19-28-31
03-11-29-32-35
14-21-24-28-33
09-14-22-23-31
03-21-26-30-31
05-15-20-27-29
02-23-24-25-26
07-13-20-24-25
03-23-26-27-28
06-20-21-26-29
01-10-14-19-35
12-18-27-32-35
02-06-24-27-28
03-08-11-21-30
09-14-20-25-31
04-13-19-21-28
10-11-12-21-31
02-07-11-20-24
06-17-25-29-30
13-23-24-26-34
09-17-21-25-26
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Forum for Physics Educators
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Forum for Physics Educators
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_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l


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Forum for Physics Educators
Phys-l@phys-l.org
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