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




On Feb 26, 2014, at 5:21 PM, Jeffrey Schnick <JSchnick@Anselm.Edu> wrote:

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

Selecting the random seed from the clock is fine for most use. For this case, it would be interesting to start with the same seed and see how often the original routine cuts out adjacent pairs.


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?

Did I not get the output formatted correctly? Can you summarize the results of the two methods in a single table?

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.

Ok, I would have thought to find a statistic per set and then figure out the probability per 21 sets from that. But you’re solving the problem more completely.

Paul