import numpy as np
import matplotlib.pyplot as plt

# %% Generating random samples with normal():

mu = 10
sigma = 5
sample_size = 100
samples = np.random.normal(mu, sigma, sample_size)

# %% Normal distribution function:

x_low = -10
x_high = 30
dx = 0.01
x_array = np.arange(x_low, x_high+dx, dx)
pdf_array = ((1/(sigma*np.sqrt(2*np.pi)))
             *np.exp(-((x_array-mu)**2/(2*(sigma**2)))))

# %% Plotting histogram of samples and normal dist function:

plt.close('all')
fig1 = plt.figure(num=1, figsize=(30/2.54, 24/2.54))#Inch

# %% Plotting normalized histogram:
num_bins = sample_size
plt.hist(samples, num_bins, density=True)

# %% Plotting normal dist function:
plt.plot(x_array, pdf_array,'r', linewidth=5)
plt.grid()
plt.title('Normalized histogram and normal distr fun')
plt.xlabel('x')
plt.ylabel('Relative occurancies and probabilty density')

# plt.savefig('plot_normal_dist.pdf')
plt.show()