Let Y and X be two random variables and let E (Y|X) conditional expectation function. Which of the following is true for the law of iterated expectations ?

I. The law says that if we take the expectation over all the values that we first condition on, we obtain the unconditional expectation

II. E [E (Y|X)] = E (Y)

III. E (Y) is the probability weighted average of all the conditional means of Y given X

Select the right answer :

a. None

b. I, II

c. II, III

d. I, II, III

e. I