Plot Probability Density of an Histogram

[scidam]

To plot probability density distribution from empirical data you need to estimate probability density first.
One of the ways to do it is to use the kernel density estimation approach (see scipy's kde density estimator).
Also, you can use ready-made function from seaborn package.

import seaborn as sns
import numpy as np
import matplotlib.pyplot as plt
x=np.random.randn(10000)                                                                                                                                                                              
sns.distplot(x) #plots histogram and kde-estimation of the pdf.
plt.show()