- #1

confused_engineer

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Hello everyone. I have a Python code which calculates, given a continuos uniform random variable U(-1,1), the order of a interpolation polynomial and a set of points the evolution of a function of this random variable. i.e.

v0 = cp.Uniform(-1,1)

t = np.linspace(0, 10, 10)

order=1

.

.

.

plt.plot (t, v0*t)

and it returns the Nodes, Weights, Mean and Variances in each of the 10 points.

I want to replicate this by hand.

I have no issue with the zeros, since I just have to find the ones of (½)*x*(5*x

Does this means that I shoud integrate (½)*x*(5*x

v0 = cp.Uniform(-1,1)

t = np.linspace(0, 10, 10)

order=1

.

.

.

plt.plot (t, v0*t)

and it returns the Nodes, Weights, Mean and Variances in each of the 10 points.

I want to replicate this by hand.

I have no issue with the zeros, since I just have to find the ones of (½)*x*(5*x

^{2}-3), but I don't know how to calculate the weights. I am following the book Numerical Methods for Stochastic Computations A Spectral Method Approach by Dongbin Xiu (page 40), where it suggests that I should write w_{j}^{(N)}=Integrate l_{j}^{(N)}wdx.Does this means that I shoud integrate (½)*x*(5*x

^{2}-3) multiplied by the random variable U(-1, 1)? Am I understanding this wrong? I don't know how to integrate a random variable...
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