Mathematics · Probability Distributions
A random variable T has a symmetric distribution if T and -T have the same distribution. Let X and Y be independent random variables. Which of the following statements is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If X has a symmetric distribution, then XY is always asymmetric
- 2X + Y is never symmetric if X and Y have the same symmetric distribution
- 3If X ~ N(3, 1) and Y ~ N(2, 2), then 2X - 3Y has a symmetric distribution
- 4If X and Y are identically distributed, then X - Y has a symmetric distribution✓
Correct answer
If X and Y are identically distributed, then X - Y has a symmetric distribution
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