2016年3月5日 · 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, 1/2, 1/4 respectively. Then variables are uncorrelated but dependent. Consider bivariate data uniform in a diamond (a square rotated 45 degrees).

2018年11月10日 · 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 does joint normality of two variables add to the knowledge of zero correlation between two variables, which leads us to conclude that these two variables MUST be independent?

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2015年9月7日 · 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 to uncorrelated, (non-)orthogonal and (un)correlated can happen at the same time.

A time-honored reminder in statistics is "uncorrelatedness does not imply independence". Usually this reminder is supplemented with the psychologically soothing (and scientifically correct)

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 question is understood!

2015年10月10日 · $\begingroup$ 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 observations y are uncorrelated". Earlier in the book (p13): "the responses are uncorrelated" because "the errors are uncorrelated". $\endgroup$ –

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2016年9月20日 · 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 of the sum of uncorrelated random variables is the sum of their variances. But what about the variance itself for a linear combination of these r.v.'s?

2015年5月26日 · 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 knowledge, and build their careers.