class_docstr: A two-way contingency table.
  
  Parameters
  ----------
  table : array_like
      A contingency table.
  shift_zeros : bool
      If True and any cell count is zero, add 0.5 to all values
      in the table.
  
  Attributes
  ----------
  table_orig : array_like
      The original table is cached as `table_orig`.
  
  See Also
  --------
  statsmodels.graphics.mosaicplot.mosaic
  scipy.stats.chi2_contingency
  
  Notes
  -----
  The inference procedures used here are all based on a sampling
  model in which the units are independent and identically
  distributed, with each unit being classified with respect to two
  categorical variables.
  
  References
  ----------
  Definitions of residuals:
      https://onlinecourses.science.psu.edu/stat504/node/86
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docstr: Returns fitted joint probabilities under independence.
  
  The returned table is outer(row, column), where row and
  column are the estimated marginal distributions
  of the rows and columns.
docstr_tok: ["Returns","fitted","joint","probabilities","under","independence",".","The","returned","table","is","outer","(","row",",","column",")",",","where","row","and","column","are","the","estimated","marginal","distributions","of","the","rows","and","columns","."]
code: def independence_probabilities(self):
      """
      Returns fitted joint probabilities under independence.
  
      The returned table is outer(row, column), where row and
      column are the estimated marginal distributions
      of the rows and columns.
      """
  
      row, col = self.marginal_probabilities
      itab = np.outer(row, col)
  
      if isinstance(self.table_orig, pd.DataFrame):
          itab = pd.DataFrame(
              itab, self.table_orig.index, self.table_orig.columns
          )
  
      return itab
  
imports: import warnings
  import numpy
  import pandas
  from scipy import stats
  from statsmodels import iolib
  from statsmodels.tools import sm_exceptions
  from statsmodels.tools.decorators import cache_readonly
label_desc: Use image node_id 7 for calling the Table obj's underlying member method code with example usage: obj.independence_probabilities() and returns: itab