def METHOD_NAME(coordinates, pce, weight=1):
    beta = pce.coefficients
    beta[0] = 0
    product = pce.polynomial_basis.evaluate_basis(coordinates)
    product = np.transpose(np.transpose(product) * weight)
    product = product.dot(beta)
    product = np.sum(product, axis=1)
    product = product ** 2
    product = product * polynomial_chaos.Polynomials.standardize_pdf(coordinates,
                                                                     pce.polynomial_basis.distributions)
    return product