Develop a function to simulate a normal distribution and provide a visual plot of it.,

Question Analysis

The question asks you to develop a function that simulates a normal distribution and to create a visual plot of it. This involves two primary tasks:

1. Simulate a Normal Distribution:

   • A normal distribution, also known as a Gaussian distribution, is a probability distribution that is symmetric about the mean. It is characterized by its bell-shaped curve.
   • To simulate a normal distribution, you typically need two parameters: the mean (average) and the standard deviation (which measures the spread or dispersion of the dataset).
   • The task involves generating random numbers that conform to these parameters.

2. Visual Plot:

   • Once the normal distribution is simulated, you need to visualize it using a plot. This can be achieved using a plotting library that can render the bell curve of the normal distribution.

Answer

To solve this problem, we can use Python along with libraries like numpy for generating the normal distribution and matplotlib for plotting it. Below is a step-by-step solution:

import numpy as np
import matplotlib.pyplot as plt

def simulate_normal_distribution(mean=0, std_dev=1, num_samples=1000):
    """
    Simulates a normal distribution and plots it.
    
    :param mean: Mean of the normal distribution.
    :param std_dev: Standard deviation of the normal distribution.
    :param num_samples: Number of samples to generate.
    """
    # Generate random data following a normal distribution
    data = np.random.normal(loc=mean, scale=std_dev, size=num_samples)
    
    # Plotting the data
    plt.figure(figsize=(8, 6))
    plt.hist(data, bins=30, density=True, alpha=0.6, color='g')
    
    # Plotting the probability density function (PDF)
    xmin, xmax = plt.xlim()
    x = np.linspace(xmin, xmax, 100)
    p = (1 / (np.sqrt(2 * np.pi) * std_dev)) * np.exp(-((x - mean) ** 2) / (2 * std_dev ** 2))
    plt.plot(x, p, 'k', linewidth=2)
    
    plt.title('Normal Distribution')
    plt.xlabel('Value')
    plt.ylabel('Frequency')
    plt.grid(True)
    plt.show()

# Example usage:
simulate_normal_distribution(mean=0, std_dev=1, num_samples=1000)

Explanation:

• Simulate Normal Distribution: We use numpy.random.normal() to generate num_samples random data points that follow a normal distribution with a specified mean and std_dev.
• Plotting: We use matplotlib.pyplot to create a histogram of the generated data, which represents the distribution. We also plot the theoretical probability density function (PDF) overlaying the histogram to illustrate the normal distribution curve.

This function provides a visual plot of the simulated normal distribution, showcasing the characteristic bell curve of the distribution.