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

posted by martin  – Austria, 2020-07-01 10:40 (951 d 05:29 ago) – Posting: # 21626
Views: 3,740

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:

UA Flag
 Admin contact
22,485 posts in 4,710 threads, 1,603 registered users;
20 visitors (0 registered, 20 guests [including 6 identified bots]).
Forum time: 15:09 CET (Europe/Vienna)

The difference between a surrogate and a true endpoint
is like the difference between a cheque and cash.
You can get the cheque earlier but then,
of course, it might bounce.    Stephen Senn

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