Step 1 — Introduction to Gaussian Distribution
A Gaussian Distribution also known as a Normal Distribution, it is characterized by its mean and standard deviation. It is a type of probability distribution where data values are centered around the mean and the spread is controlled by the standard deviation.
Mathematical Expression:
Step 2 — Importing Required Libraries
Before we begin, import the necessary libraries like numpy, scipy.stats and matplotlib.pyplot.
Step 3 — Generating a Gaussian Random Variable (RV) with 50 Samples
Let’s start by generating a Gaussian random variable with 50 samples using the norm.rvs function from the scipy.stats module.
Step 4 — Calculating Mean and Standard Deviation
Calculate and display the mean and standard deviation of the generated random variable.
Step 5— Visualizing the Probability Distribution
Create a histogram to visualize the probability distribution of the generated random variable.
Step 6 — Generating a Gaussian Random Variable with Custom Parameters
Generate another Gaussian random variable with 5,000 samples, specifying the center (loc) and spread (scale) values.
Step 7 — Displaying Mean and Standard Deviation for the Second RV
Print the mean and standard deviation of the second generated random variable.
Step 9 — Visualizing the Probability Distribution
for the Second RV Create a histogram to visualize the probability distribution of the second generated random variable using a larger number of bins.
Conclusion:
In this article, we explored the concept of Gaussian distributions. We learned how to generate Gaussian random variables with different parameters using Python and visualize their probability distributions using histograms. Gaussian distributions play a crucial role in statistics and data analysis due to their prevalence in real-world data and remember to run the provided code snippets in a Python environment to observe the results and visualizations described in each step.
