Normal (Gaussian) Distribution

📊 Normal (Gaussian) Distribution in Python

The Normal Distribution (also called Gaussian distribution) is a bell-shaped curve where most of the data points cluster around the mean. It’s widely used in statistics, machine learning, and natural phenomena modeling.

1. Characteristics of Normal Distribution

Symmetric about the mean
Mean, median, and mode are equal
Defined by mean (μ) and standard deviation (σ)
Probability Density Function (PDF):

$\frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$

2. Generate Normal Distribution Using NumPy

import numpy as np
import matplotlib.pyplot as plt# Parameters
mu = 0 # mean
sigma = 1 # standard deviation
size = 1000 # number of samples# Generate random numbers
data = np.random.normal(mu, sigma, size)

# Display first 10 numbers
print(data[:10])

import numpy as np

import matplotlib.pyplot as plt# Parameters

mu = 0 # mean

sigma = 1 # standard deviation

size = 1000 # number of samples# Generate random numbers

data = np.random.normal(mu, sigma, size)

# Display first 10 numbers

print(data[:10])

3. Visualize Normal Distribution

Histogram

Using Seaborn

kde=True → plots the smooth density curve

4. Generate Normal Distribution with Different Mean & Std

5. Check Mean and Standard Deviation

6. Probability Density Function (PDF)

🧠 Summary

Parameter	Meaning
`mu` / `loc`	Mean (center of the distribution)
`sigma` / `scale`	Standard deviation (spread)
`size`	Number of random samples

Use numpy.random.normal() for generating data
Use matplotlib or seaborn for visualization
The bell curve is symmetric and widely applicable in statistics

🎯 Practice Task

Generate 1000 numbers with μ=100 and σ=15
Plot histogram with KDE
Verify mean and standard deviation of the generated data
Plot the corresponding PDF curve

Normal (Gaussian) Distribution