MATLAB Implementation of Standard Normal Distribution with Code Examples

In the MATLAB programming environment, we can develop code to generate random numbers following various probability distributions. Beyond the standard normal, Poisson, and Rayleigh distributions mentioned, there are additional distributions like exponential and chi-square distributions that can be implemented. These distributions have extensive applications across fields including finance, physics, biology, and engineering. Therefore, mastering random number generation for these distributions in MATLAB is essential for technical computing. During code development, understanding the probability density functions and cumulative distribution functions of different distributions is crucial. Programmers must also proficiency with MATLAB's built-in random number generation functions such as randn() for standard normal distribution, poissrnd() for Poisson distribution, and raylrnd() for Rayleigh distribution. These functions implement sophisticated algorithms - for instance, randn() uses the polar method or Ziggurat algorithm to transform uniform random numbers into normally distributed values. Through continuous practice and code debugging, developers can deepen their understanding of these distributions and optimize implementations according to specific requirements, such as adjusting distribution parameters or improving computational efficiency.