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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 mean_hub_height(self):
 r""" Calculates the mean hub height of the wind turbine cluster. The mean hub height of a wind turbine cluster is necessary for power output calculations with an aggregated wind turbine cluster power curve. Hub heights of wind farms with higher nominal power weigh more than others. Assigns the hub height to the turbine cluster object. Returns ------- self Notes ----- The following equation is used [1]_: .. math:: h_{WTC} = e^{\sum\limits_{k}{ln(h_{WF,k})} \frac{P_{N,k}}{\sum\limits_{k}{P_{N,k}}}} with: :math:`h_{WTC}`: mean hub height of wind turbine cluster, :math:`h_{WF,k}`: hub height of the k-th wind farm of the cluster, :math:`P_{N,k}`: installed power of the k-th wind farm References .. [1] Knorr, K.: "Modellierung von raum-zeitlichen Eigenschaften der Windenergieeinspeisung für wetterdatenbasierte Windleistungssimulationen". Universität Kassel, Diss., 2016, p. 35 """

        self.hub_height = np.exp(sum(
            np.log(wind_farm.hub_height) * wind_farm.get_installed_power() for
            wind_farm in self.wind_farms) / self.get_installed_power())
        return self