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


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

Complete thread:

 Admin contact
20,801 posts in 4,354 threads, 1,446 registered users;
online 21 (1 registered, 20 guests [including 13 identified bots]).
Forum time: 09:17 CEST (Europe/Vienna)

Medical statistician: One who will not accept that Columbus discovered America…
because he said he was looking for India in the trial plan.    Stephen Senn

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz