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

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?

» 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?

—

Pass or fail!

ElMaestro

Pass or fail!

ElMaestro

### Complete thread:

- Statistical independence, what is it? I mean really, what is it?? ElMaestro 2020-06-27 21:35 [General Statistics]
- 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