Suppose that you has to guess given a set of numbers
- If they are random.
- The mathematical expectation
Is there a definition of randomness that allow this prove/test?
Is even possible? if so: How many value would be enough ?
If numbers come from a coin experiment, results could be coded as 0 or 1,
Then how many "bits" are enough to "test" variable randomness?
According to the law of large numbers, the average of the results (adding the results and dividing by the number of trials) should become closer and closer to the expected value as more trials are performed.
But if we don't know where those numbers come from then we don't know what to expect!
What are the law of large numbers hypothesis?
Does the definition of random cointain a reference to average and to the expected value?
It is deeply confusing to me,
thanks in advance for any information