Simple examples of uncorrelated but not independent $X$ and $Y$
Mar 5, 2016 · The variables are uncorrelated but dependent. Alternatively, consider a discrete bivariate distribution consisting of probability at 3 points (-1,1),(0,-1),(1,1) with probability 1/4, …
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 exactly …
correlation - What does it mean for two variables to be …
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What is the relationship between orthogonal, correlation and ...
Sep 7, 2015 · Here is the relationship: If X and Y are uncorrelated, then X-E[X] is orthogonal to Y-E[Y]. Unlike that independent is a stronger concept of uncorrelated, i.e., independent will lead …
probability - For which distributions does uncorrelatedness imply ...
A time-honored reminder in statistics is "uncorrelatedness does not imply independence". Usually this reminder is supplemented with the psychologically soothing …
Uncorrelated/orthogonal random vectors - Cross Validated
Correlation and orthogonality, although closely related concepts, are not the same things. This question is confusing because both answers are correct, depending on which version of the …
what does it mean for a single variable to be uncorrelated?
Oct 10, 2015 · $\begingroup$ here is an example from my textbook (p19, 5th ed, Montgomery, Peck Vining): in the derivation of Var[b], Var distributes across the summation "because the …
In practice, how to clearly prove that variables are uncorrelated?
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
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 variance …
Why are principal component scores uncorrelated?
May 26, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …