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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 gauss_distribution(function_variable, standard_deviation, mean=0):
 r""" Gauss distribution. The Gauss distribution is used in the function :py:func:`~.power_curves.smooth_power_curve` for power curve smoothing. Parameters function_variable : float Variable of the gaussian distribution. standard_deviation : float Standard deviation of the Gauss distribution. mean : Float Defines the offset of the Gauss distribution. Default: 0. Returns ------- pandas.Series or numpy.array Wind speed at hub height. Data type depends on the type of `wind_speed`. Notes ----- The following equation is used [1]_: .. math:: f(x) = \frac{1}{\sigma \sqrt{2 \pi}} \exp \left[-\frac{(x-\mu)^2}{2 \sigma^2}\right] with: :math:`\sigma`: standard deviation, :math:`\mu`: mean References .. [1] Berendsen, H.: "A Student's Guide to Data and Error Analysis". New York, Cambridge University Press, 2011, p. 37 """

    return (1 / (standard_deviation * np.sqrt(2 * np.pi)) *
            np.exp(-(function_variable - mean)**2 /
                   (2 * standard_deviation**2)))