Mathematics · Probability and Statistics
Let X 1 , ..., X 12 be a random sample from the N(2, 4) distribution and Y 1 , ..., Y 15 be a random sample from the N(-2, 5) distribution, where the two samples are mutually independent. Let X̄ and Ȳ be the sample means, and S 1 2 , S 2 2 be the sample variances. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The distribution of 2√3(Ȳ + 2) S 1 is t 14
- 2The distribution of 5 S 1 2 4 S 2 2 is F 11, 14✓
- 3The distribution of 1 20 (55S 1 2 + 56S 2 2 ) is χ 2 26
- 4The distribution of X̄ + Ȳ is N(0, 2 3 )
Correct answer
The distribution of 5 S 1 2 4 S 2 2 is F 11, 14
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