Question

(or Gaussian) probability P(x) where, dr is the variance and μ is the mean. 1. Define the array x as the numbers x--5,-4.....5 2. Use numpy to evaluate px) using x and Name these arrays p-a, p.b, and p-c, respective ly.

How is this done using python programming?

Answer 1

#Loading Libraries
import numpy as np
import math

#Define Probability Density Function
def p_x(x, mu, sigma_square):
A = math.sqrt(2 * math.pi * sigma_square)
B = float(((x - mu) ** 2)) / sigma_square
C = -(float(B)/2)
value = math.exp(C) / A
return value

#Question 1:
x = np.array([-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5])

#Question 2:
# (a)
p_a = np.zeros(len(x))
for i in range(len(x)):
p_a[i] = p_x(x[i], mu = 0, sigma_square=1)

print(p_a)

# (b)
p_b = np.zeros(len(x))
for i in range(len(x)):
p_b[i] = p_x(x[i], mu = 1, sigma_square=1)

print(p_b)

# (c)
p_c = np.zeros(len(x))
for i in range(len(x)):
p_c[i] = p_x(x[i], mu = 0, sigma_square=2)

print(p_c)

** For any confusion or answer mismatch please comment.