## Die don’t remember the last roll. Really. [General Statistics]

❝ If it did remember the last roll and the outcome was somehow a function of it, wouldn't that be correlation?

Well, the die is

**Thick As A Brick**. If a roll depends on the result of the last one, that could be (a) cheating by an expert gambler or (b) an imperfect die. In both cases you would have a correlation indeed and the concept collapses.

❝ And how is the die and last roll mental image fitting in with Z and s being indepedent? I think it fits better into the mental picture of errors in a model being IID.

My example deals with \(\small{\mathcal{N}(\mu,\sigma^2)}\). If you want to dive into combinatorics/permutations (coin flipping, rolling dice) see the first example in this post.

❝ Or more generally:

❝ From a sample of size N I am deriving two quantities A and B. Under what cicumstances will A and B be independent? A die with Alzheimer does not really shed light on it, does it?

As usual: Know the data generating process. If you cannot be sure that the outcome of B is independent from A you are in deep shit.

❝ Kindly help me a little more. I do not see the idea of the R code but it executes nicely …

- Simulate a \(\small{\mathcal{N}(\mu,\sigma^2)}\) population \(\small{x}\) with \(\small{\mu=100},\) and \(\small{\sigma=20}\).

For \(\small{N=10^5}\) the trusted Mersenne-Twister gives us \(\small{\hat{\mu}=100.0655,}\) \(\small{\hat{\sigma}=20.0154}\).

Draw a histogram of \(\small{x}\). Overlay the histogram with a normal curve.

- Draw 30 samples \(\small{x_{s1},x_{s2},\ldots,x_{s30}}\) of size 20 from \(\small{x}\).

Estimate \(\small{\bar{x}, {s_{x}}^{2}}\) of each sample and plot the normal curves with \(\small{\bar{x}\mp s_x}\).

Get pooled estimates, which acc. to the CLT should approximate the population’s parameters.

- Compare the outcome with the population.

- Correlation of samples’ means and variances. As expected, there is none.

❝ … except errors for `idx.m`

and `idx.v`

.

Fuck. Try the edited one.

❝ Code on this forum rarely provides clarity for me. This has nothing to do with the code, but has everything to do with me

Sorry. I added more comments than usual.

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### 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