Q60Section ST (Statistics (Q11–Q65))60 of 65

Projection quadratic forms for N_3(0, I_3)

Let $Y = (Y_1, Y_2, Y_3)^T \sim N_3(0, I_3)$ , where $I_3$ denotes the identity matrix of order 3. Let $A = \begin{pmatrix} \frac13 & \frac13 & \frac13 \ \frac13 & \frac13 & \frac13 \ \frac13 & \frac13 & \frac13 \end{pmatrix}$ and $B = I_3 - A$ . Let $\chi_1^2$ denote chi-square distribution with 1 degree of freedom. Then which of the following statements is/are correct?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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