Question:
Let (X, Y) be a discrete random vector. Then which of the following statements is/are true ?
Let (X, Y) be a discrete random vector. Then which of the following statements is/are true ?
Updated On: Oct 1, 2024
- If X and Y are independent, then X2 and |Y| are also independent.
- If the correlation coefficient between X and Y is 1, then P(Y = aX + b) = 1 for some a, b ∈ \(\R\)
- If X and Y are independent and E[(XY)2] = 0, then P(X = 0) = 1 or P(Y = 0) = 1
- If Var(X) = 0, then X and Y are independent
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The Correct Option is A, B, C, D
Solution and Explanation
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.
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