Simulated (Fair And Unfair) Coin Tosses

In this student project it was to be experimentally figured out how<br> fair a fair coin behaves. To achieve this, fair coin tosses with a different number of maximum coin tosses<br> were simulated and it was analyzed how often chains of given lengths of<br> ones/zeros (assumed to be heads/tails) appear and how much more often<br> zeros appear per experiment compared to ones. This maximum number was<br> - 10 tosses per experiment<br> - 100 tosses per experiment<br> - 1.000 tosses per experiment<br> - 10.000 tosses per experiment<br> - 100.000 tosses per experiment<br> - 1.000.000 tosses per experiment<br> - 10.000.000 tosses per experiment<br> - 100.000.000 tosses per experiment<br> - 1.000.000.000 tosses per experiment<br> - 10.000.000.000 tosses per experiment Except for the last three, all experiments were repeated 1.000 times.<br> The 100.000.000 tosses per experiment was repeated 100 times, the 1.000.000.000<br> tosses per experiment was repeated 10 times and the 10.000.000.000 tosses per<br> experiment was NOT repeated. For these one/zero chain distributions the fitting parameters were determined,<br> assuming a geometrical distribution. <br> The experiments with up to 100.000.000 tosses per experiment were repeated<br> with an UNFAIR coin, using a Maxwell Boltzmann statistic for the distribution<br> of coin tosses. -------------------------------------------------- In the data-folder these experiments are divided into the normal distributed<br> and Maxwell-Boltzmann distributed coin toss experiments. These two folders contain the folders with the data for the different<br> maximum number of coin tosses per experiment. Each of these folders contains two subfolders which contain the distributions<br> of the respective chains of ones or zeros (heads or tails). In this folder (NOT the subfolders!) in addition can be found:<br> - a file with the fitting parameters for each heads/tails-chain-distribution,<br> - a file with an analysis of these fitting parameters,<br> - a file in which it is analyzed how much more often zero was the result of<br> the toss (for one experiment)<br> - a file with an analysis of that,<br> - and two files in which the chain-distributions are summed up. The result for each coin toss in each experiment were NOT saved. <br> For the Maxwell Boltzmann distributed coin tosses also the distribution<br> itself was saved for each experiment and can be found in the respective<br> subfolder. -------------------------------------------------- In the scripts folder, all the programs can be found that were created<br> to create and analyze all the data. All programs are published as free software under the<br> GNU General Public License version 3 as published by the<br> Free Software Foundation -------------------------------------------------- ATTENTION:<br> The .tar.gz-file contains more than 35000 files.<br> It may take a while to extract all the files.