Mathematics · Statistical Inference
Let ((X1, Y1), (X2, Y2), ..., (X10, Y10)) be a random sample from a bivariate normal distribution BVN(μ1, μ2, σ12, σ22, ρ) with μ1 = 5, μ2 = 6, σ12 = 4, σ22 = 9 and ρ = 1/2. Then, which of the following statements is true?
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- 1The distribution of (2 ∑ (Yi - 6)2 [sum from i = 1 to 3]) / ∑ (Yi - 6)2 [sum from i = 4 to 9] is F-distribution with 3 and 6 degrees of freedom
- 2The distribution of (2√2 (X1 - 5)) / √∑(Xi - 5)2 [sum from i = 3 to 10] is t-distribution with 9 degrees of freedom
- 3The distribution of 1√7 ∑ (Xi - Yi + 1) [from i = 1 to 10] is χ2-distribution with 10 degrees of freedom
- 4The distribution of 1√7 ∑ (Xi - Yi + 1) [from i = 1 to 10] is N(0, 10)✓
Correct answer
The distribution of 1√7 ∑ (Xi - Yi + 1) [from i = 1 to 10] is N(0, 10)
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