TITLE: probability and statistics: Does having little correlation imply independence?
QUESTION [16 upvotes]: Suppose there are two correlated random variable and having very small correlation coefficient (order of 10-1). Is it valid to approximate it as  independent random variables?

REPLY [6 votes]: The correlation coefficient only measures linear dependence of two random variables. So if they depend on each other in a non-linear way, the correlation coefficient will not catch it.