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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 generate_synthetic_observation_trajectory(self, length, initial_Pi=None):
 """Generate a synthetic realization of observables. Parameters length : int Length of synthetic state trajectory to be generated. initial_Pi : np.array of shape (nstates,), optional, default=None The initial probability distribution, if samples are not to be taken from equilibrium. Returns ------- o_t : np.array of shape (nstates,) of dtype=np.float32 The trajectory of observations. s_t : np.array of shape (nstates,) of dtype=np.int32 The trajectory of hidden states, with each element in range(0,nstates). Examples -------- Generate a synthetic observation trajectory for an equilibrium realization. Use an initial nonequilibrium distribution. """

        # First, generate synthetic state trajetory.
        s_t = self.generate_synthetic_state_trajectory(length, initial_Pi=initial_Pi)

        # Next, generate observations from these states.
        o_t = self.output_model.generate_observation_trajectory(s_t)

        return [o_t, s_t]