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I am confused with respect to these two terms. In a book on regression analysis, I read the following statements.

1. For two normally distributed variables, zero covariance / correlation means independence of the two variables.

2. With the normality assumption, the following equation means that [tex] \mu_i [/tex] and [tex] \mu_j [/tex] are NOT ONLY uncorrelated BUT ALSO independently distributed.

[tex] \left \mu_i - N (0, \sigma^2 \right) [/tex]

Not able to get the wiggly line (~) after ui

I am trying to understand if it is possible to have two variables that are

(a) uncorrelated, and not-independent.

(b) uncorrelated and independent

(c) correlated and not-independent

(d) correlated and independent

I would appreciate it if you could explain each type with one example.

Thanks

MG.

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# Uncorrelated Vs. Independent variables

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