Changes

Random variables must be functions to the real numbers, so it is ambiguous what the statement "populations of species can randomly drift away from their 'mean'" is intended to mean without a quantification.  Nevertheless, using height as a characteristic to measure for the sake of argument, it is clear why the law of large numbers does not hold.  If we observe the height of a randomly selected member of a population each year, the observations are random variables.  Nevertheless, evolutionists would provide two explanations for why the law of large numbers does not hold in this experiment.  First, evolutionists would argue that factors like [[genetic drift]] allow for the events of one time period to affect the height distribution of a population in future time periods.  Second, evolutionists would suggest that trends in random height suggest precisely the conclusion that the distribution of population heights is changing with each year, indicating that the random variables are not identically distributed.  This suggests precisely the conclusion that the population is changing over time.  By the way, looking at the statement of the weak law of large numbers, it is clear that if the random variables are not identically distributed (especially if they do not have the same mean), then the "mean" <math>\mu</math> in the statement of the theorem is completely meaningless, mathematically.  [[User:GregG|GregG]] 23:06, 14 March 2012 (EDT)

Random variables must be functions to the real numbers, so it is ambiguous what the statement "populations of species can randomly drift away from their 'mean'" is intended to mean without a quantification.  Nevertheless, using height as a characteristic to measure for the sake of argument, it is clear why the law of large numbers does not hold.  If we observe the height of a randomly selected member of a population each year, the observations are random variables.  Nevertheless, evolutionists would provide two explanations for why the law of large numbers does not hold in this experiment.  First, evolutionists would argue that factors like [[genetic drift]] allow for the events of one time period to affect the height distribution of a population in future time periods.  Second, evolutionists would suggest that trends in random height suggest precisely the conclusion that the distribution of population heights is changing with each year, indicating that the random variables are not identically distributed.  This suggests precisely the conclusion that the population is changing over time.  By the way, looking at the statement of the weak law of large numbers, it is clear that if the random variables are not identically distributed (especially if they do not have the same mean), then the "mean" <math>\mu</math> in the statement of the theorem is completely meaningless, mathematically.  [[User:GregG|GregG]] 23:06, 14 March 2012 (EDT)