# i.i.d. random vectors [duplicate]

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:

1. $$E(X_1)=E(X_2)$$ and $$E(Y_1)=E(Y_2)$$ (the same for variance);
2. Both, $$X_1$$ and $$Y_1$$, are independent of $$X_2$$ and $$Y_2$$ .

$$2Cov(X_1,Y_1)=E[(X_1-X_2)(Y_1-Y_2)]$$.