Statistical independence, what is it? I mean really, what is it?? [General Sta­tis­tics]

posted by ElMaestro  – Belgium?, 2020-07-01 09:42  – Posting: # 21628
Views: 761

Thanks Martin,

» Two random variables X and Y are independent if and only if the events {X ≤ x} and {Y ≤ y} are independent for all x and y, that is, F(x, y) = F X (x)F Y (y), where F(x, y) is the joint cumulative distribution function and F X and F Y are the marginal cumulative distribution functions of X and Y, respectively.

thanks for the posts.
I think now we are in the right direction, not confounding independence with correlation.
Given a sample x1,x2....xn, from which we estimate mean and variance, would we under the quote above consider the estimated mean and the estimated variance "random variables" in their own right, or is this immaterial to the issue at hand?

I could be wrong, but...

Best regards,
ElMaestro

"Pass or fail" (D. Potvin et al., 2008)

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