Assignment no. 4. Practical Assignments on Statistical / Algorithmic Data Modeling

Objective:

To develop skills in statistical data modeling, hypothesis testing, classification and regression

algorithms, model evaluation techniques, and hands-on exercises with the scikit-learn library.

4.1: Hypothesis Testing and Probability Distributions

2. Probability Distributions:

o Visualize the probability distribution of a dataset using histograms and probability density functions (PDFs).

A Python program to visualize the probability distribution of a dataset using histograms and probability density functions (PDFs). 

Program:

import numpy as np

import matplotlib.pyplot as plt

import seaborn as sns

# Step 1: Generate or provide sample data

data = np.random.normal(loc=50, scale=10, size=1000)  # Example: 1000 data points with mean 50 and standard deviation 10

# Step 2: Create a histogram and overlay a KDE plot

sns.histplot(data, bins=30, kde=True, color='purple')

# Step 3: Label the graph

plt.title("Probability Distribution of Sample Data")

plt.xlabel("Value")

plt.ylabel("Frequency")

plt.show()

Output:

The output will be a plot that looks similar to this:

• Histogram: The bars represent how frequently each range of values appears in the dataset.

• KDE Plot (Smooth Curve): The curve overlays the histogram and shows the probability density function (PDF), indicating where the data values are most concentrated.

When you run this program, you will see a graph with a smooth bell-shaped curve overlaid on a histogram. This is typical for data that follows a normal distribution, where the mean is at the center of the peak, and the spread indicates the standard deviation.

Explaination:

Generate Sample Data:

• np.random.normal(loc=50, scale=10, size=1000): This generates 1000 data points from a normal distribution with a mean of 50 and a standard deviation of 10. You can replace this with your own dataset.

Histogram and KDE Plot:

• sns.histplot(data, bins=30, kde=True, color='purple'): This line creates a histogram and overlays a Kernel Density Estimate (KDE) plot, which provides a smooth probability density function (PDF).

Labeling and Display:

• Titles and axis labels are added for better understanding, and the plot is displayed using plt.show().