Hi:
If two events are statistically independent, then they are correlated.
That is, the correlation coefficient or covariance is not zero.
However, even if two events are statistically correlated, independence is not guaranteed.
A question is are there some special cases that we are sure that correlation implies independence????
Another question is what are the examples that two events are correlated but not independent????
Since our events are obtained from sampling, how do we design/choose a sampling process that produces two independent events?
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