Mathematics · Multivariate Analysis
Let X = X1X2 be a bivariate random vector with covariance matrix Σ = 1 √2√2 2. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The first principal component based on Σ is 1√3(X1 + √2X2)
- 2sup { aTΣa : a ∈ ℝ2 and aTa = 1 } = 3✓
- 3The second principal component based on Σ explains exactly 10% of the total variability
- 4The first principal component based on Σ explains exactly 90% of the total variability
Correct answer
sup { aTΣa : a ∈ ℝ2 and aTa = 1 } = 3
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