GATE 2024 ST – Question 20
Which statement is not true for random variables X,Y?
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Correct answer: (D) Independent X²,Y² imply independent X,Y.
Explanation
Take X=Y to be a nondegenerate fair sign ±1. Their squares are both constant 1 and hence independent, while X,Y themselves are perfectly dependent, refuting D. Independent continuous variables with equal distributions verify A,B. Measurable functions of independent variables remain independent, verifying C. **D**.