GATE 2025 ST – Question 30

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

X is 10-dimensional N₁₀(0,I). Let Y=ln√(XᵀX) and M_Y(t)=E(e^(tY)),t>−10. Find M_Y(2) (integer).

Show answer and explanation

Correct answer: 10 to 10

Explanation

e^(2Y)=XᵀX, a χ²₁₀ variable with mean 10. Therefore **M_Y(2)=10**.

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