Question

Let (X, Y) be a discrete random vector. Then which of the following statements is/are true ?

• A. If X and Y are independent, then X2 and |Y| are also independent.
• B. If the correlation coefficient between X and Y is 1, then P(Y = aX + b) = 1 for some a, b ∈ $\R$
• C. If X and Y are independent and E[(XY)2] = 0, then P(X = 0) = 1 or P(Y = 0) = 1
• D. If Var(X) = 0, then X and Y are independent

Answer 1

Answer: (A), (B), (C), (D)

If X and Y are independent, then X2 and |Y| are also independent.

Answer 2

The correct option is (A) : If X and Y are independent, then X2 and |Y| are also independent, (B) : If the correlation coefficient between X and Y is 1, then P(Y = aX + b) = 1 for some a, b ∈ $\R$, (C) : If X and Y are independent and E[(XY)2] = 0, then P(X = 0) = 1 or P(Y = 0) = 1 and (D) : If Var(X) = 0, then X and Y are independent.