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

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Paul Nord
Sent: Wednesday, February 26, 2014 5:47 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my institution (
math challenge)

Is this with the same random seed?
No. The old code results you give were those of Brian Whatcott who ran the code on MatLab. I have only recently learned how to copy characters from an MS-Dos window for pasting here. So I gave a summary of my results from one run. Here is my old summary:
I ran a Monte Carlo Octave function to investigate occurrences of sequences of 2 numbers in a row and, occurrences of round numbers (10,20,30). In a million sets of 21 rows of five numbers between 1 and 35 inclusive, I got 2784 cases in which there were exactly 2 round numbers and only 133 cases in which there were exactly 2 sequences of 2 numbers in a row. In 0 out of a million cases there were both 2 or fewer round numbers and 2 or fewer sequences of 2 numbers in a row. The first set given in this thread met both of these conditions. In 11 cases out of a million there were both 3 or fewer whole numbers and 3 or fewer sequences of 2 numbers in a row.

Also:
Quote from "Octave Help":
By default, the generator is initialized from `/dev/urandom' if it
is available, otherwise from cpu time, wall clock time and the
current fraction of a second.
End Quote

If this is the same random seed, it is
pretty obvious where you've cut the tail of the distribution.
Please explain. The results look pretty much the same to me. I still don't get this cutting of the tail business. In the old code I threw out duplicates. How does that cut the tail? I thought the distribution was supposed to be flat. What do you mean by a tail in this context?



It does look like some of your most improbable events became more
frequent. But something that happens two times out of a million may need a
larger statistical sample to be convincing.

Why are you summing over sets of 21?
There were 21 students. See the thread-starter post.


Paul


On Feb 26, 2014, at 3:50 PM, Jeffrey Schnick <JSchnick@Anselm.Edu> wrote:

Old Code:
getdist(1000000)
totalrounds = 49 482 2723 9827 25707 52175 86488
totalseq2 = 0 14 136 739 2712 7811 18039
total = 0 0 0 18 147 1063 5289

Here are the results with the new code:

octave-3.2.4.exe:13> getdist2(1000000)
totalrounds = 46 436 2662 9580 25606 52869 87332
totalseq2 = 2 17 143 787 2708 7775 18031
total = 0 0 1 9 161 1120 5359

Elapsed time is 14113 seconds.
-----------------
Key:
Each result is 21 sets of 5 unique numbers between 1 and 35 inclusive.
totalrounds(1) = number of results with zero round numbers (10,20,30)
totalrounds(2) = number of results with one round number.
totalrounds(i) = number of results with i-1 round numbers.

totalseq2(1) = number of results with zero sequences of two numbers in a
row.
totalseq2(2) = number of results with one sequence of two numbers in a
row.
totalseq2(i) = number of results with i-1 sequences of two numbers in a
row.

total(1) = number of results with zero round numbers and zero sequences
of two numbers in a row.
total(2) = number of results with one OR FEWER round numbers and one
OR FEWER sequences of two numbers in a row.
total(i) = number of results with i-1 OR FEWER round numbers and i-1 OR
FEWER sequences of two numbers in a row.
------------------------
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_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l