Gaussian random values. Experiment with the following function for generating random variables from the Gaussian distribution, which is based on generating a random point in the unit circle and using a form of the Box-Muller formula.

def gaussian(): r = 0.0 while (r >= 1.0) or (r == 0.0): x = -1.0 + 2.0 * random.random() y = -1.0 + 2.0 * random.random() r = x*x + y*y return x * math.sqrt(-2.0 * math.log(r) / r)

Take a command-line argument n and generate n random numbers, using an array a [ ] of 20 integers to count the numbers generated that fall between i * .05 and (i+1) * .05 for i from 0 to 19. Then use stddraw to plot the values and to compare your result with the normal bell curve.

Here's the Python code for the program so far:

import sys import stdio import random import math import numpy as np import matplotlib.pyplot as plt plt.rcParams["patch.force_edgecolor"] = True import statistics

# function header def gaussian(): r = 0.0 while (r >= 1.0) or (r == 0.0): x = -1.0 + 2.0 * random.random() y = -1.0 + 2.0 * random.random() r = x*x + y*y return x * math.sqrt(-2.0 * math.log(r) / r)

# command line for n integers n = int(sys.argv[1])

# store n random numbers using gaussian() distribution random_numbers = [] for i in range(n): random_numbers.append(gaussian())

# print random_numbers array stdio.writeln(random_numbers)

a = [] for i in range(20): count = 0 for j in random_numbers: if i*0.5 < j < (i+1)*0.5: count += 1 a.append(count)

stdio.writeln(a)

# mean emp_mean = np.mean(a) # standard deviation emp_stdev = np.std(a) # Plot a histogram of your sample with the absolute number of counts for each bin. Choosing 25 bins. m, bins, patches = plt.hist(a, 25, facecolor='g', alpha=0.5) plt.xlabel('Probability of success') plt.ylabel('Number of trials') plt.title('Histogram') plt.grid(True) plt.show()

# Plot a histogram of your standard sample with the normal counts to form a probability density. # Compare your histrogram with the density of the standard normal distribution by inserting its density into the histogram plot. Choosing 25 bins. # b = [] Needed??? for i in range(0, len(a)): a.append((a[i] - emp_mean)/emp_stdev)

m, bins, patches = plt.hist(a, 25,facecolor='g', alpha=0.5,density = True,label='standardized sample') stnm = np.random.standard_normal(100000) m, bins, patches = plt.hist(stnm, 25,facecolor='r', alpha=0.5,density = True,label='standard normal dist') plt.legend() plt.xlabel('Standard Deviation') plt.ylabel('Normalized counts') plt.title('Histogram') plt.grid(True) plt.show()

It appears as if I can run the code using the command line argument, an array a[] of 20 integers between the given condition from 0 to 19. The matplotlib module shows the bell curve comparison. I wasn't able to implement stddraw module. That's as far as I can solve for this assignment. I appreciate your coding assistance to produce the assignment's result!