Sample mean and sample variance

Question

The sample mean is $\bar X = \frac{1}{n}\sum_{i=1}^n X_i$ and the sample variance is $S^2 = \frac{1}{n-1} \sum_{i=1}^n (X_i - \bar X)^2$

Can someone please explain how the sample mean and sample variance are independent?

Is this a question from a course or textbook? If so, please add the [self-study] tag & read its wiki. — gung - Reinstate Monica, Apr 30 '16 at 23:27
Are you sure you're not missing an assumption? Under the appropriate additional assumption(s), a few seconds with Google will reveal many proofs on the internet, including on this site. — Mark L. Stone, Apr 30 '16 at 23:28
Please follow @gung's advice and let us know whether this is a self-study question. It's somewhat unclear what you are asking at the moment - are you asking what conditions are needed for the sample mean and variance to be independent, or are you asking for a proof that they are independent, but did not realise this required additional assumptions to hold? — Silverfish, Apr 30 '16 at 23:57
@Analyst1 I made a typo adding the Latex - it was actually correct in the original picture. Fixed now. — Silverfish, May 01 '16 at 00:35
Its a proof questions, we just have to show why the two are independent — Blueberry, May 01 '16 at 01:16
Possible duplicate of What is the most surprising characterization of the Gaussian (normal) distribution? — Xi'an, May 01 '16 at 11:46

score 1 · Answer 1 · answered May 01 '16 at 00:15

1

The premise of the question is false - they aren't independent, in general.

Here's an example:

answered May 01 '16 at 00:15

Glen_b

1 Answers1