def predict_expectation(self, X, ancillary_X=None):
        """
        Predict the expectation of lifetimes, :math:`E[T | x]`.

        Parameters
        ----------
        X: numpy array or DataFrame
            a (n,d) covariate numpy array or DataFrame. If a DataFrame, columns
            can be in any order. If a numpy array, columns must be in the
            same order as the training data.
        ancillary_X: numpy array or DataFrame, optional
            a (n,d) covariate numpy array or DataFrame. If a DataFrame, columns
            can be in any order. If a numpy array, columns must be in the
            same order as the training data.

        Returns
        -------
        percentiles: DataFrame
            the median lifetimes for the individuals. If the survival curve of an
            individual does not cross 0.5, then the result is infinity.


        See Also
        --------
        predict_median
        """
        lambda_, rho_ = self._prep_inputs_for_prediction_and_return_scores(X, ancillary_X)
        return pd.DataFrame((lambda_ * gamma(1 + 1 / rho_)), index=_get_index(X))