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## Wednesday, July 13, 2011

### Random times Random is not Random

Some things in Mathematics are counterintuitive, well at least surprising. The first thing I think of is that there are different 'infinities'. Try to explain to your neighbor that the number of even numbers is equal to the number of numbers divisible by three. Or that there are more points on the ( real number ) line between 0 and than there are integers.

Or this one. Random times is Random not Random? Not uniformly random to be precise. In the experiment below I threw a coin with sides 0 and 1 99,999 times. The first graph shows the number of 0s and 1s thrown. Practically equal at 50,000. Then I did the same with two coins 99,999 times but multiplied the product ( mod 2 ). The second graph shows the result. 75,000 zero's and 25,000 1s.

 Click to enlarge
Now imagine the same for any number. A number ends with 0,1,2,..., or 9. The number of 0s,1s, 2s will be equal if you take a large set of random numbers. But if you multiply two random numbers the last digits will not have a uniform distribution.

Interesting is that the distribution depends on the type of operation.

Tally@(RandomInteger[1, {10^7}])
Tally@(RandomInteger[1, {10^7}] RandomInteger[1, {10^7}])

2) The results make sense. If you look at the Tally results, for multiplying them together, 25% are 1, 75% are zero. This is because 0*0=0, 0*1=0, and 1*0=0, while only 1*1=1. So, on average, 3/4 of the results will be zero and 1/4 will be 1.

2. 1) Did not know Tally, thanks, interesting.

2) My conclusion too. Therefore the graphs.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)