Mathematics · Probability and Statistics

Let the random vector (X1, X2, X3)T have a positive definite dispersion matrix given by 1ρρρ1ρρρ1. Then, which of the following statements is true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1The variance of the first principal component is 1 + 2ρ for any ρ
2The second principal component can explain more than 32% of the total variation for any ρ
3The first principal component can only explain 32% of the total variation for some ρ
4ρ may be -0.47✓

Correct answer

ρ may be -0.47

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