# Creating Gaussian Plot Function
def gaussianPlotter(vector):
    """
    Calculates and plots a Gaussian Probability Density Function (PDF)

    Parameters
    ----------
    vector : array-like, shape (n_samples, n_features)

    Returns
    -------
    output : matplotlib plt.plot()
    """
    mean = vector.mean()
    std_dev = vector.std()
    normal_pdf = (1/np.sqrt(2*np.pi*std_dev**2))*np.exp(-((vector.sort_values() - mean)**2)/(2*std_dev**2))
    plt.plot(vector.sort_values(), normal_pdf, color= 'red', label= 'Normal PDF')

# Creates the figure, title, and labels
# Plots a Frequency distribution along w/ a Kernel Density Estimate
plt.figure(figsize= (10,5))

## Gaussian Kernel is used to estimate a Gaussian PDF
sns.distplot(features_DSH, bins= 10, kde= True, color= '#1f77b4',
             kde_kws= {'kernel': 'gau', 'label': 'KDE: Estimated PDF',
                       'color': 'black', 'lw': 3})

## Gaussian PDF plotting function
gaussianPlotter(features_DSH)

## Plot Labels
plt.title('Frequency & Probability Distribution of Study Times');
plt.ylabel('Kernel Density Estimate');
plt.xlim(25, 71)
plt.legend(loc= 'best')