Simple examples of uncorrelated but not independent $X$ and $Y$
Mar 5, 2016 · A two-sentence answer: the clearest case of uncorrelated statistical dependence is a non-linear function of a RV, say Y = X^n. The two RVs are clearly dependent but yet not …
correlation - Uncorrelatedness + Joint Normality = Independence.
Nov 10, 2018 · However, two variables that are uncorrelated AND jointly normally distributed are guaranteed to be independent. Can someone explain intuitively why this is true?
What is the relationship between orthogonal, correlation and ...
Sep 7, 2015 · The vector is no longer orthogonal to Y. If two variables are uncorrelated they are orthogonal and if two variables are orthogonal, they are uncorrelated. Correlation and …
Why are principal component scores uncorrelated? - Cross Validated
May 26, 2015 · Why are principal component scores uncorrelated? Ask Question Asked 10 years, 6 months ago Modified 10 years, 6 months ago
Variance of Uncorrelated Variables - Cross Validated
Sep 20, 2016 · Now there are a few things regarding uncorrelated variables that obviously play into this: - Two random variables are said to be uncorrelated if their Cov (X,Y)=0 - The …
How does PCA behave when there is no correlation in the dataset?
Jul 19, 2021 · If the true underlying covariance matrix is the identity: the leading eigen vectors of the sample correlation matrix will point in random directions, rather than directions that are …
what does it mean for a single variable to be uncorrelated?
Oct 10, 2015 · In the simple linear regression model, y=a+bx+e, e is assumed to be uncorrelated. Accordingly, y is uncorrelated. I understand that two variables are uncorrelated if their …
regression - Why do the residuals have to be uncorrelated with the ...
Aug 9, 2017 · In linear regression, the residuals have to be uncorrelated with the predictor variable. Is it true, and if it, why is that?
Uncorrelated/orthogonal random vectors - Cross Validated
Can't comment. While the 2nd definition seems better, doesn't an inner product need to output a real number since that's the field that the vector space of random variables are defined over?
If X and Y are uncorrelated, are X^2 and Y also uncorrelated?
Sep 9, 2017 · Being uncorrelated is a necessary but not sufficient condition for being independent. So if two variables $X$ and $Y$ are uncorrelated but dependent, then $f (X)$ …