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

posted by martin  – Austria, 2020-07-01 08:40  – Posting: # 21626
Views: 945

Dear ElMaestro,

I know this is might be confusing where you may find the corresponding mathematical proof of interest.


Here is another follow up on the definition of statistical independence - its a concept in probability theory. A very nice summary can be found here:

Two events A and B are statistical independent if and only if their joint probability can be factorized into their marginal probabilities, i.e., P(A ∩ B) = P(A)P(B). If two events A and B are statistical independent, then the conditional probability equals the marginal probability: P(A|B) = P(A) and P(B|A) = P(B).

Now applying this concept to random variables:

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.


best regards & hope this helps

Martin


Edit: Merged with a later (now deleted) post. You can edit your OP for 24 h. [Helmut]

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