General Studies · Bivariate Normal Distribution
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 = 12. Then, which of the following statements is true?
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- 1The distribution of 2 ∑i=13 (Yi - 6)2∑i=39 (Yi - 6)2 is an F-distribution with 3 and 6 degrees of freedom
- 2The distribution of 2√2(X1 - 5)√∑i=310 (Xi - 5)2 is a t-distribution with 9 degrees of freedom
- 3The distribution of ∑i=110 (Xi - Yi - 11)2 is a χ2 distribution with 10 degrees of freedom
- 4The distribution of 1√7 ∑i=110 (Xi - Yi + 1) is N(0, 10)✓
Correct answer
The distribution of 1√7 ∑i=110 (Xi - Yi + 1) is N(0, 10)
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