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RegisterStatistical independence, what is it? I mean really, what is it?? [General Statistics]
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]
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]
Complete thread:
- Statistical independence, what is it? I mean really, what is it?? ElMaestro 2020-06-27 21:35 [General Statistics]
![[Mix]](https://static.bebac.at/img/mix.png "open in Mix view")
- Die don’t remember the last roll. Really. Helmut 2020-06-28 13:35
- Die don’t remember the last roll. Really. ElMaestro 2020-06-28 14:45
- Die don’t remember the last roll. Really. Helmut 2020-06-28 15:36
- Still none the wiser ElMaestro 2020-06-28 18:20
- You’ve lost me now. Helmut 2020-06-28 21:55
- Worded differently ElMaestro 2020-06-29 08:30
- Still not sure what you are aiming at… Helmut 2020-06-29 16:46
- Still not sure what you are aiming at… ElMaestro 2020-06-30 00:55
- Confuse-a-Cat Helmut 2020-06-30 11:33
- Confuse-a-Cat ElMaestro 2020-06-30 13:07
- Confuse-a-Cat Helmut 2020-06-30 14:27
- pseudorandom and linear independence mittyri 2020-07-01 00:04
- Confuse-a-Cat ElMaestro 2020-06-30 13:07
- Confuse-a-Cat Helmut 2020-06-30 11:33
- Still not sure what you are aiming at… ElMaestro 2020-06-30 00:55
- Still not sure what you are aiming at… Helmut 2020-06-29 16:46
- Worded differently ElMaestro 2020-06-29 08:30
- You’ve lost me now. Helmut 2020-06-28 21:55
- Still none the wiser ElMaestro 2020-06-28 18:20
- Die don’t remember the last roll. Really. Helmut 2020-06-28 15:36
- Die don’t remember the last roll. Really. ElMaestro 2020-06-28 14:45
- Statistical independence, what is it? I mean really, what is it??martin 2020-07-01 08:40
- Statistical independence, what is it? I mean really, what is it?? ElMaestro 2020-07-01 09:42
- Statistical independence, what is it? I mean really, what is it?? martin 2020-07-01 10:07
- Statistical independence, what is it? I mean really, what is it?? ElMaestro 2020-07-01 09:42
- Die don’t remember the last roll. Really. Helmut 2020-06-28 13:35
Ing. Helmut Schütz