Let mathbf Y=beginpmatrixy1y2y3endpmatrixsim N3(mathbf 0,mathbf I3) and mathbf A=1/3beginpmatrix2&-1&-1-1&2&-1-1&-1&2endpmatrix. What is the value of Var(mathbf Y'mathbf Amathbf Y)?

Q53Section I (Objective (Q1–Q80))52 of 79

Multivariate Analysis — variance of a quadratic form in normal variates

Let $\mathbf Y=\begin{pmatrix}y_1\\y_2\\y_3\end{pmatrix}\sim N_3(\mathbf 0,\mathbf I_3)$ and $\mathbf A=\frac{1}{3}\begin{pmatrix}2&-1&-1\\-1&2&-1\\-1&-1&2\end{pmatrix}$ . What is the value of $\mathrm{Var}(\mathbf Y'\mathbf A\mathbf Y)$ ?

Pick an option to check your answer. In a mock test a wrong answer here costs 0.83 mark.

Keyboard: A–D answer · S solution · ←/→ previous/next