GATE 2020 ST – Question 32

Multivariate Analysis · Multivariate Normal and Wishart Distributions · 1 mark · Numerical answer

A centred4-vector has covariance matrix with diagonal1 and every off-diagonal entry0.5. Find the proportion of total variation explained by its first two principal components(two decimals).

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Correct answer: 0.75 to 0.75 OR 75 to 75

Explanation

The covariance is0.5I+0.5J. The all-ones eigenvector has eigenvalue0.5+0.5(4)=2.5; three orthogonal contrasts have eigenvalue0.5. Total variance is4 and the first two contribute2.5+0.5=3. Proportion=3/4=0.75; the key also accepts75 as a percentage alternative.

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