Q. What is the difference between uncorrelation and independence?
Uncorrelation means that there is no linear dependence between the two random variables, while independence means that no types of dependence exist between the two random variables. For example, in the figure below \(Y_1\) and \(Y_2\) are uncorrelated (no linear relationship) but not independent.
This means that independent random variables are always uncorrelated, but uncorrelated random variables may not be independent. In other words, independence is a stronger statement than uncorrelation.