Imagine you draw (independently) an infinite amount of draws from a random variable with infinite support, and the strong law of large numbers applies. We know the average for sure will be equal to the mean. Can we further say that, since the size of the sample is infinity, the distribution of the draws will be exactly the distribution of the random variable?
2026-03-29 06:07:51.1774764471
Does the law of large numbers pin down the distribution of an infinite sample?
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