r"""
        Compute the expected lifetime, :math:`E[T]`, using covariates X. This algorithm to compute the expectation is
        to use the fact that :math:`E[T] = \int_0^\inf P(T > t) dt = \int_0^\inf S(t) dt`. To compute the integral, we use the trapizoidal rule to approximate the integral.

        Caution
        --------
        However, if the survival function doesn't converge to 0, the the expectation is really infinity and the returned
        values are meaningless/too large. In that case, using ``predict_median`` or ``predict_percentile`` would be better.

        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.

        Returns
        -------
        expectations : DataFrame

        Notes
        -----
        If X is a DataFrame, the order of the columns do not matter. But
        if X is an array, then the column ordering is assumed to be the
        same as the training dataset.

        See Also
        --------
        predict_median
        predict_percentile

def predict_expectation(self, X):
        r"""
        Compute the expected lifetime, :math:`E[T]`, using covariates X. This algorithm to compute the expectation is
        to use the fact that :math:`E[T] = \int_0^\inf P(T > t) dt = \int_0^\inf S(t) dt`. To compute the integral, we use the trapizoidal rule to approximate the integral.

        Caution
        --------
        However, if the survival function doesn't converge to 0, the the expectation is really infinity and the returned
        values are meaningless/too large. In that case, using ``predict_median`` or ``predict_percentile`` would be better.

        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.

        Returns
        -------
        expectations : DataFrame

        Notes
        -----
        If X is a DataFrame, the order of the columns do not matter. But
        if X is an array, then the column ordering is assumed to be the
        same as the training dataset.

        See Also
        --------
        predict_median
        predict_percentile

        """
        subjects = _get_index(X)
        v = self.predict_survival_function(X)[subjects]
        return pd.DataFrame(trapz(v.values.T, v.index), index=subjects)