Suppose X = (X1, X2, X3, X4)T has a multivariate normal N4(0, I2 ⊗ Σ), where I2 is the 2 × 2 identity matrix, ⊗ is the Kronecker product, and Σ = \(\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\right]\). Define Z = \(\left(\begin{array}{ll} \rm X_1 & \rm X_2 \\ \rm X_3 & \rm X_4\end{array}\right)\) and Q = ((Qij)) = ZTZ. Suppose \(\rm χ_n^2\) denotes a chi-square random variate with n degrees of freedom, and Wm(n, Σ) denotes a Wishart distribution of order m with parameters n and Σ. The distribution of (Q11 + Q12 + Q21 + Q22) is

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CSIR UGC (NET) Mathematical Science: Held On (7 June 2023)
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  1. W1(2, 2)
  2. W1(1, 2)
  3. W1(2, 1)
  4. \(2\rm χ_n^2\)

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Option 1 : W1(2, 2)
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