Time for action – drawing a normal distribution

We can generate random numbers from a normal distribution and visualize their distribution with a histogram (see https://www.khanacademy.org/math/probability/statistics-inferential/normal_distribution/v/introduction-to-the-normal-distribution). Draw a normal distribution with the following steps:

1. Generate random numbers for a given sample size using the normal() function from the random NumPy module:

   N=10000
   normal_values = np.random.normal(size=N)

2. Draw the histogram and theoretical PDF with a center value of 0 and standard deviation of 1. Use matplotlib for this purpose:

   _, bins, _ = plt.hist(normal_values, np.sqrt(N), normed=True, lw=1)
   sigma = 1
   mu = 0
   plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) ),lw=2)
   plt.show()

   In the following diagram, we see the familiar bell curve:

   

What just happened?

We visualized the normal distribution using the normal() function from the random NumPy module. We did...