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I know that for answering this question I have to calculate the double integral of $f(x,y)=ce^{-2x^2-8y^2}$ and set it to $1$. Someone told me to use the gamma distribution function but I don’t know how.

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This is a multivariate normal distribution with $\mathbf\mu=\mathbf0$ and $\mathbf\Sigma^{-1}=\begin{bmatrix}4&0\\0&16\end{bmatrix}$. Thus $$c=\frac1{\sqrt{(2\pi)^k\det\mathbf\Sigma}}=\frac1{2\pi\sqrt{1/64}}=\frac4\pi$$ where $k=2$ is the number of variables.

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  • $\begingroup$ Could you explain a bit more please ? $\endgroup$
    – Pegi
    Oct 12, 2019 at 18:04
  • $\begingroup$ @Pegi This is basically pattern recognition... $\endgroup$ Oct 13, 2019 at 2:29

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