# Linked Questions

14 questions linked to/from Covariance and independence?
0 votes
1 answer
595 views

### Covariance matrices and independency [duplicate]

If we have a diagonal covariance matrix does that guarantee independency?
• 241
53 votes
7 answers
60k views

### Why zero correlation does not necessarily imply independence

If two variables have 0 correlation, why are they not necessarily independent? Are zero correlated variables independent under special circumstances ? If possible, I am looking for an intuitive ...
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50 votes
8 answers
86k views

### Simple examples of uncorrelated but not independent $X$ and $Y$

Any hard-working student is a counterexample to "all students are lazy". What are some simple counterexamples to "if random variables $X$ and $Y$ are uncorrelated then they are independent"?
16 votes
4 answers
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### Can somebody illustrate how there can be dependence and zero covariance?

Can somebody illustrate, as Greg does, but in more detail, how random variables can be dependent, but have zero covariance? Greg, a poster here, gives an example using a circle here. Can somebody ...
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4 votes
5 answers
462 views

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1 answer
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1 answer
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### Independence of random variables and its relation to the expectation

For sochastic processes $X_n$ and $Y_n$ it holds that if they are indenpendant for all $n$ then $$E[X_nY_n] = E[X_n]E[Y_n]$$ But can you go the other way. I mean if $E[X_nY_n] = E[X_n]E[Y_n]$, does ...