Question: Suppose $left(x_{1}, X_{2}, X_{3} ight)^{T}$ is a random vector with a distribution having the density $$ frac{1}{(2 pi)[3 / 2}} exp left( frac{1} {2}left(2 x_{1}^{2}+2

$Suppose $\left(x_{1}, X_{2}, X_{3} ight)^{T}$ is a random vector with a$

Suppose $\left(x_{1}, X_{2}, X_{3} ight)^{T}$ is a random vector with a distribution having the density $$ \frac{1}{(2 \pi)"[3 / 2}} \exp \left( \frac{1} {2}\left(2 x_{1}^{2}+2 x_{2}^{2}+x_{3}^{2}-2 x_{1} X_{2}-2 x_{2} x_{3} ight) ight) \text { for }\left(x_{2}, x_{2), x_{3} ight) \in \mathbf {R}^{3} $$ Calculate the covariance of $X_{1}$ and $X_{3}$. Give your answer as a decimal correct to one decimal place. SP.PC.118

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