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Part CCSIR NET December 2024two-thirds-is-just-under-seventy-percent

Two thirds is just under seventy percent

If (X1,X2)(X_{1}, X_{2})ᵗ ~ N2((0,0)N_{2}((0, 0)ᵗ, [[3, 1], [1, 3]]), then which of the following statements are true?

  1. A.The distribution of the second principal component is normal with mean 0 and variance 2.✓ Correct
  2. B.The variance of the first principal component is 4.✓ Correct
  3. C.The first principal component explains more than 70% of the total variance.
  4. D.The correlation coefficient between the first and the second principal components is 0.✓ Correct

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: If every marginal is normal then the vector is multivariate normal

More on this topic

The chapter behind this: Multivariate normal and Wishart — free to read

From Linear Models and Multivariate › Multivariate normal distribution

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