NO.PZ2020010304000004
问题如下：
If X1 and X2 are uncorrelated (Corr[X1, X2] = 0), are they independent?
解释：
No.
There are many ways that two random variables can be dependent but not correlated. For example, if there is no linear relationship between the variables but they both tend to be large in magnitude (of either sign) at the same time. In this case, there may be tail dependence but not linear dependence (correlation). The image below plots realizations from a dependent bivariate random variable with 0 correlation. The dependence in this distribution arises because if X1 is close to 0 then X2 is also close to 0.
