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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 LogNormal(x, a, mu, sigma):
 """PDF of a log-normal distribution Inputs: ------- ``x``: independent variable ``a``: amplitude ``mu``: center parameter ``sigma``: width parameter Formula: -------- ``a/ (2*pi*sigma^2*x^2)^0.5 * exp(-(log(x)-mu)^2/(2*sigma^2)) """

    return a / np.sqrt(2 * np.pi * sigma ** 2 * x ** 2) *\
        np.exp(-(np.log(x) - mu) ** 2 / (2 * sigma ** 2))