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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def predict(self, X, with_noise=True):
 """ Predictions with the model. Returns posterior means and standard deviations at X. Note that this is different in GPy where the variances are given. Parameters: X (np.ndarray) - points to run the prediction for. with_noise (bool) - whether to add noise to the prediction. Default is True. """

        m, v = self._predict(X, False, with_noise)
        # We can take the square root because v is just a diagonal matrix of variances
        return m, np.sqrt(v)