Independent vs. Uncorrelated Random Variables

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Independent random variables exhibit no dependence whatsoever, while uncorrelated random variables lack linear dependence but may still have nonlinear relationships. For instance, two independent variables, like the roll of a die and the flip of a coin, do not influence each other at all. Conversely, uncorrelated variables might include a quadratic relationship, where their correlation is zero despite a dependency. Understanding these distinctions is crucial in statistical analysis and modeling. The discussion highlights the importance of recognizing the nuances between independence and uncorrelation in probability theory.
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Hello,

What is the difference between independent and uncorrelated random variables? Practical examples of both?

Regards
 
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If variables are uncorrelated they have no _linear_ dependence, but they might have a dependence that is nonlinear. If variables are independent they have no dependence at all.
 
mXSCNT said:
If variables are uncorrelated they have no _linear_ dependence, but they might have a dependence that is nonlinear. If variables are independent they have no dependence at all.

Can you elaborate more with examples, please?

Thanks in advance
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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