# -*- coding: utf-8 -*-
"""
Created on Wed Dec  8 13:25:03 2021

@author: Sim
"""

import matplotlib.pyplot as plt
import numpy as np
import matplotlib

matplotlib.rcParams["text.usetex"] = True

x = np.linspace(-3,5,100)
y0 = 1/(2*np.pi)**2 * np.exp (-x**2/2)
y1 = 1/(2*np.pi)**2 * np.exp (-(x-2)**2/2)
plt.plot(x,y0, label='$N(\mu_1, \sigma^2)$')
plt.plot(x,y1, label='$N(\mu_2, \sigma^2)$')
fx = r'$$f(x)=\frac{1}{\sqrt{2\pi}\sigma} \exp\Bigg\{-\frac{(x-\mu)^2}{2\sigma^2}\Bigg\} $$'
plt.title(fx, fontsize=18, color='r')
plt.axvline(x=0, color='b', linestyle=':')
plt.text(0.1,.005, r'\Large$\mu_1$=0')
plt.axvline(x=2, color='b', linestyle=':')
plt.text(2.1,.005, r'\Large$\mu_2$=2')
plt.legend()