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Statistical Analysis & Pattern Matching
If I have a set of random data, which could be the result of rolling a 6 sided die 1,000 times, and the die is favored to rolls 2 numbers more often than the others, how do I analyze the data to determine which numbers it favors without knowing in advance that it favors any of the numbers? Considering I am looking at random data it is impossible to say if the dice favors any number for sure, but I can assume that it favors a number and check to see which numbers it would favor if it did. That is an example of the type of problem I want to solve but I can think of others. How about an algorithm that generates random numbers between 1 and 1,000,000. Lets say I have a database of 10 million numbers it has generated, and want to determine what numbers it favors. This is not the same question as asking if it is random data, because for our purposes it is random. This is just asking if it is more likely to produce certain number. Lets say for this example that the machine is programmed to never produce the same number twice, until it has randomly generated every other possible number. Is there a way to predict this is happening by looking at the data? Normally the gamblers fallacy isn't a useful idea, but in this case it would help you know in advance what the machine will generate because that is how it is programmed. How would I solve these problems using mathematica?