Two random variables X and Y are independently distributed if all of the following conditions hold,with the exception of
A)Pr(Y = y = x)= Pr(Y = y).
B)knowing the value of one of the variables provides no information about the other.
C)if the conditional distribution of Y given X equals the marginal distribution of Y.
D)E(
Y)= E[E(Y )].

Question

Two random variables X and Y are independently distributed if all of the following conditions hold,with the exception of
A)Pr(Y = y = x)= Pr(Y = y). 
B)knowing the value of one of the variables provides no information about the other. 
C)if the conditional distribution of Y given X equals the marginal distribution of Y. 
D)E(
Y)= E[E(Y )].

Quizplus · Accepted Answer

Options A, B, and C are all conditions of independence between two random variables. Option D is incorrect because it is the definition of the law of iterated expectation, which is not a condition for independence. Therefore, the exception is option D.

Two Random Variables X and Y Are Independently Distributed If