Computer

"One usually uses a programming language like Python along with libraries such as pandas, matplotlib, and scipy. Some of the code snippets and steps to achieve it are:

Assuming that one have the required libraries installed, so, to perform the tasks:

import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

from scipy.stats import norm

from scipy.optimize import minimize

# Load the CSV file

data = pd.read_csv(""ArgyleSquarePedestWalkbysCSVFile.csv"")

# Extract pedestrian count data

pedestrian_counts = data[""PedestrianCount""]

# 1.1) Plot histogram

plt.hist(pedestrian_counts, bins=15, edgecolor='black', alpha=0.7)

plt.title(""Histogram of Pedestrian Counts"")

plt.xlabel(""Pedestrian Count"")

plt.ylabel(""Frequency"")

plt.show()

# 1.2) Fit a single Gaussian model

def negative_log_likelihood(params, data):

    mu, sigma = params

    return -np.sum(norm.logpdf(data, loc=mu, scale=sigma))

# Initial guess for parameters

initial_params = [np.mean(pedestrian_counts), np.std(pedestrian_counts)]

# Find MLE of parameters using optimization

result = minimize(negative_log_likelihood, initial_params, args=(pedestrian_counts,))

mu_mle, sigma_mle = result.x

# Create a range of x values for the density plot

x_range = np.linspace(min(pedestrian_counts), max(pedestrian_counts), 1000)

# Plot histogram and Gaussian density

plt.hist(pedestrian_counts, bins=15, density=True, alpha=0.7, label=""Histogram"")

plt.plot(x_range, norm.pdf(x_range, loc=mu_mle, scale=sigma_mle), 'r', label=""Gaussian Fit"")

plt.title(""Histogram and Gaussian Fit"")

plt.xlabel(""Pedestrian Count"")

plt.ylabel(""Density"")

plt.legend()

plt.show()

# Output MLE of parameters

print(f""Mean (μ) MLE: {mu_mle}"")

print(f""Standard Deviation (σ) MLE: {sigma_mle}"")

"