Two random variables X and Y are independently distributed if all of the following conditions hold, with the exception of
A)Pr(Y = y $\mid X$ = 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 $\mid X$ )].

Question

Quizplus · Accepted Answer

The exception is D) E(Y) = E[E(Y | X)], which is a property of the law of total expectation, not a condition that defines independence between two random variables. Independence is characterized by the fact that the probability distribution of one variable is not affected by the knowledge of the other variable, as described in options A, B, and C.

Two Random Variables X and Y Are Independently Distributed If ∣X\mid X∣X

Two Random Variables X and Y Are Independently Distributed If $\mid X$