code: def test_overdispersed_bound(probs, overdispersion):
      total_count = torch.tensor(
          [1, 2, 5, 10, 20, 50, 1e2, 1e3, 1e5, 1e6, 1e7, 1e8]
      )
      d = binomial_dist(
          total_count, probs, overdispersion=overdispersion
      )
      relative_error = d.variance.sqrt() / (
          probs * (1 - probs) * total_count
      )
  
      # Check bound is valid.
      assert (relative_error >= overdispersion).all()
  
      # Check bound is tight.
      assert relative_error[-1] / overdispersion < 1.05
  
imports: import math
  import pytest
  import torch
  from torch.distributions.transforms import SigmoidTransform
  import pyro.distributions
  from pyro.contrib.epidemiology import beta_binomial_dist, binomial_dist, infection_dist
  from pyro.contrib.epidemiology.distributions import _RELAX_MIN_VARIANCE, set_relaxed_distributions
  from tests.common import assert_close
label_desc: Use image node_id 6 for calling a global function with example usage: test_overdispersed_bound(probs, overdispersion) without return types