code: def test_reductions_with_start_state(stream):
      example = cudf.DataFrame({"name": [], "amount": []})
      sdf = DataFrame(stream, example=example)
      output0 = (
          sdf.amount.mean(start=(10, 2)).stream.gather().sink_to_list()
      )
      output1 = sdf.amount.count(start=3).stream.gather().sink_to_list()
      output2 = sdf.amount.sum(start=10).stream.gather().sink_to_list()
  
      df = cudf.DataFrame(
          {"name": ["Alice", "Tom", "Linda"], "amount": [50, 100, 200]}
      )
      stream.emit(df)
  
      assert output0[0] == 72.0
      assert output1[0] == 6
      assert output2[0] == 360
  
imports: import json
  import operator
  import numpy
  import pandas
  import pytest
  from dask.dataframe.utils import assert_eq
  from distributed import Client
  from streamz import Stream
  from streamz.dask import DaskStream
  from streamz.dataframe import Aggregation, DataFrame, DataFrames, Series
label_desc: Use image node_id 39 for calling a global function with example usage: test_reductions_with_start_state(stream) without return types