Question: Suppose that $X$ and $y$ are random variables whose joint density is given by $$ f_{X Y)(x, y)=frac{1}{pi sqrt{3}} exp left(- frac{2}{3}left(x^{2}+y^{2}-x y ight ight)

Suppose that $X$ and $y$ are random variables whose joint density

Suppose that $X$ and $y$ are random variables whose joint density is given by $$ f_{X Y)(x, y)=\frac{1}{\pi \sqrt{3}} \exp \left(- \frac{2}{3}\left(x^{2}+y^{2}-x y ight ight) \text { for }(x, y) \in \mathbf {R}^{2} $$ Calculate the value of the expectation $$ \mathrm{E} [\exp (2 X+Y)] $$ SP.PC.1161

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