Why do the mean and the variance have no predictive power for a discrete uniform distribution?
Can someone please explain this to me? Not sure I understand the point. Eg. For a fair 6-sided die with mean 3.5 and variance 105/36, what is the statement above saying? I get that 3.5 is not a possible realizable value, is that the point?
Each time you roll a die, the probability of an outcome is 1/6. It makes no sense to calculate the mean, because each rolling is an independent event. If you get 6 on the first try, you still have 1/6 probability to get 6 on the second try and so on.
Variance is calculated based on deviations from the mean, so it doesn't make sense neither.