Quadrature Example

Consider Gauss quadrature for a uniformly distributed random variable $X\sim \mathcal{U}(-1,1)$.

The roots of the corresponding second order, i.e. $n_{qu}=2$, polynomial read $x^{(1)}=-\frac{1}{\sqrt{3}}$ and $x^{(2)}=\frac{1}{\sqrt{3}}$. Compute the corresponding weights and write down the equation to compute the expected value for the model function $Y=\mathcal{M}(X)=2x^2+3$.

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