This question already has an answer here:
If $(X_1,Y_1), (X_2,Y_2)$ are independent random vectors having the same joint distribution function $F$, then is it correct to say:
- $E(X_1)=E(X_2)$ and $E(Y_1)=E(Y_2)$ (the same for variance);
- Both, $X_1$ and $Y_1$, are independent of $X_2$ and $Y_2$ .
Please argue the answer.
This question arose when I read the equality in my book:
Thanks in advance.