Difference between revisions of "Chance News 27"

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Submitted by John Gavin.
 
Submitted by John Gavin.
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==A probability problem==
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IBM has a monthly "Ponder This Challenge" which is often a probability problem. The  [http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/challenges/April2007.html April 2007 Challenge]  was the following random walk problem. 
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<blockquote>This month's puzzle concerns a frog who is hopping on the integers from minus infinity to plus infinity. Each hop is chosen at random (with equal probability) to be either +2 or -1. So the frog will make steady but irregular progress in the positive direction. The frog will hit some integers more than once and miss others entirely. What fraction of the integers will the frog miss entirely? Please find an exact answer.<br>
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Update, 4/20/07: You may consider the answer to be the limit as N goes to infinity of the fraction of integers between -N and N a frog starting at -N and randomly hopping as described misses on average. Also an answer correct to six decimal places is good enough.</blockquote>
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We invite readers to ponder this problem.

Revision as of 18:36, 15 May 2007

Quotation

I could prove God statistically. Take the human body alone - the chances that all the functions of an individual would just happen is a statistical monstrosity.

George Gallup

This is from an ineresting article about the life of George Gallup: "The Human Yardstick", Williston Rich, Saturday Evening Post January 21,1939, p. 71. The article ends with:

His greatest delution is that he can forecast the stock market. his greatest fear, that a competitor will enter his field and be dishonest with the figures. His greatest devotion, to his family, his home and his church. He says "I could prove God statistically--.

Forsooth

The following Forsooths were in the May 2007 RSS News:

The Times leader of 28 February tells us that taking regular dose of certain vitamins 'can actually increase the risk of mortality by five per cent'. Since the "risk of mortality' is already 100 percent this is very worrying.

AWF Edwards
Cambridge

How to own a random number

God created the integers; all else is the work of man, Leopold Kronecker

AACS is the copy protection technology used on HD-DVD and Blu-ray discs. The consortium that owns this technology are apparently trying to stop websites and newspapers publishing a specific 128-bit integer that, with suitable software, enables the decryption of video content on most existing HD-DVD and Blu-ray discs. As part of this effort, they have claimed ownership of the encryption key, which means that you cannot use, without written permission, that particular 30-digit integer (in base 10) and several million other unknown keys that they apparently are claiming ownership of. Not only that, but the numbers in question were chosen randomly so there is no simple way of knowing if your random choice conflicts with theirs, even if they were known publicly.

Further reading

Did we mention that a shiny new integer would make a perfect Mother’s Day gift?

Submitted by John Gavin.

A probability problem

IBM has a monthly "Ponder This Challenge" which is often a probability problem. The April 2007 Challenge was the following random walk problem.

This month's puzzle concerns a frog who is hopping on the integers from minus infinity to plus infinity. Each hop is chosen at random (with equal probability) to be either +2 or -1. So the frog will make steady but irregular progress in the positive direction. The frog will hit some integers more than once and miss others entirely. What fraction of the integers will the frog miss entirely? Please find an exact answer.
Update, 4/20/07: You may consider the answer to be the limit as N goes to infinity of the fraction of integers between -N and N a frog starting at -N and randomly hopping as described misses on average. Also an answer correct to six decimal places is good enough.

We invite readers to ponder this problem.