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Q-1A

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#Q 1A


import numpy as np

from scipy.integrate import quad

import matplotlib.pyplot as plt



# Defining the Gaussian Function


def Gaussian(mu, sigma, x):

    return (1./(np.sqrt(2*np.pi)*sigma)) * np.exp(-(x-mu)**2/(2*sigma**2))


x = np.linspace(-5,5,1001)


mu = 0

sigma = 0.5


# Plotting the Gaussian Function


plt.plot(x, Gaussian(mu,sigma,x), label=''r'$\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$')

plt.xlabel('x')

plt.ylabel('f(x)')

plt.title("Ques. 1A Gaussian Function")

plt.legend()

plt.savefig("1A.png", dpi=600)

plt.show()



# Evaluating the Integral


mu = 1

sigma = 0.5



def f(x):

    return (1./(np.sqrt(2*np.pi)*sigma)) * np.exp(-(x-mu)**2/(2*sigma**2))



x = np.linspace(-5,5,1001)

result_1 = quad(f, -np.inf, np.inf)

result_2 = 1./(sigma * np.sqrt(2*np.pi)) * result_1[0]


print("Value of the integral is = ", result_2)

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