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I am working with generalized polynomial chaos. To represent a Normal random variable, the Hermite polynomials are used. However, as far as I understand, these represent N(0,1); if what I have read is correct, if I want to work with any other mean and variance, I shoud simply use the fact that Z=(X-μ)/σ and find the new polynomials (X) substituting the regular ones (Z), which would be: 1, Z, (Z

^{2}-1)... which would mean that X

_{1}= σZ-μ and X

_{2}=σ(Z

^{2}-1)-μ...

Can someone please tell me if I am right?

Thanks.