MATLAB Random Number Generation Example: Uniform and Normal Distributions

This MATLAB example demonstrates three different random number generation methods using built-in MATLAB functions. The methods include [0,1] uniform distribution, N(0,1) standard normal distribution, and n-number of N(a,b) normal distributions. For the [0,1] uniform distribution implementation, MATLAB's rand() function generates uniformly distributed random numbers between 0 and 1 using pseudorandom number generation algorithms. For the N(0,1) normal distribution implementation, MATLAB's randn() function produces Gaussian-distributed random numbers with mean 0 and standard deviation 1, using algorithms like the Ziggurat or Box-Muller transform for efficient generation. For generating n-number of N(a,b) normal distribution samples, developers can use the transformation method: first generate standard normal variables using randn(), then apply linear transformation by multiplying by standard deviation b and adding mean a. This approach utilizes the property that linear transformations of normal variables remain normally distributed, allowing flexible parameter specification while maintaining statistical properties. Each method includes proper scaling and parameter handling to ensure accurate statistical distributions, with MATLAB providing vectorized implementations for efficient bulk generation of random numbers.