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I have a machine that generates 16 character long sentences made up of (I think kinda) random letters. I can get it to spit out up to 1 million such sentences before I loose the ability to store them (as there will be too many by then). From the million, there is not a single duplicate sentence detected. They are all different.
Is there a way I can infer at least how many possible unique sentences the machine might be capable of generating? I am testing the hypothesis whether the sentences are made from totally random characters, or do some sentences repeat?
It is possible that the generated sentences /characters are not random or have strong correlations. I don't know and that is the purpose of this experiment. I think that it's a bit of a count-distinct problem, but I can actually store a million sentences so have not used the min hash or hyperloglog technique. It takes too long to generate more than a million sentences anyway.
Is this an impossible test? I had thought that if totally random, there should be some collisions (or not) and this might be some sort of indicator with a confidence interval. Hence the Birthday Problem approach.
It's difficult for me to phrase the question without revealing the true nature of this experiment, as it would just get marked off-topic. So please bear with me.