code: def test_conflicting_noiseless_ivw(self) -> None:
      means = np.array([1, 2, 1])
      variances = np.array([0, 0, 1])
  
      new_mean, new_var = inverse_variance_weight(means, variances)
      self.assertEqual(new_mean, 1.5)
      self.assertEqual(new_var, 0.0)
  
      with self.assertRaises(ValueError):
          inverse_variance_weight(
              means, variances, conflicting_noiseless="raise"
          )
  
imports: from itertools import product
  import numpy
  import pandas
  from ax.core.data import Data
  from ax.utils.common.testutils import TestCase
  from ax.utils.stats.statstools import inverse_variance_weight, marginal_effects, relativize, relativize_data, unrelativize
label_desc: Use image node_id 5 for calling the InverseVarianceWeightingTest obj's underlying member method code with example usage: obj.test_conflicting_noiseless_ivw() without return types