MATLAB Script for Generating Gaussian Distributed Random Variables

This MATLAB script generates Gaussian distributed random variables. Using this script, you can easily produce random variables following a Gaussian distribution. The Gaussian distribution, also known as normal distribution, is a probability distribution widely present in nature. It exhibits a bell-shaped curve that is symmetric about the mean, with larger standard deviations resulting in flatter curves. Gaussian distribution finds extensive applications in statistics, natural sciences, social sciences, and various other fields. This MATLAB script implements two primary methods for Gaussian random variable generation: the Central Limit Theorem approach and the Inverse Transform Method. The script generates uniform random numbers using MATLAB's rand() function and transforms them into Gaussian distributed numbers through mathematical operations. The implementation includes: - Parameter customization for mean (mu) and standard deviation (sigma) - Vectorized operations for efficient batch generation - Proper scaling and shifting to achieve desired distribution characteristics You can modify the script parameters, such as mean and standard deviation values, to generate random variables tailored to your specific requirements. The script demonstrates key MATLAB functions including rand() for uniform random number generation and sqrt()/log() for mathematical transformations in the Box-Muller implementation variant. For deeper understanding of Gaussian distributions and random variable generation techniques, we recommend consulting relevant textbooks or online resources on probability theory and statistical computing.