A company has to test that two of its products are safe. Product two tests more favorably than product one, for both rats and guinea pigs.

As this is true, prove that this statement is correct or incorrect:

Product two has a higher total success rate on all subjects tested. (If true, prove it is true. If false, show a counterexample.)

Now, If E[Y|X] = 1, prove or disprove the following two statements:

1.E[XY] = E[X]

2.Var[XY]Var[X]