Graphical Representations of Probability Density Functions Generated Using MATLAB Code for Reference

The graphical representations of various probability density functions generated using MATLAB code are provided for reference purposes. When utilizing these visualizations to describe and understand the distribution of random variables, additional factors must be considered, including distribution characteristics, parameters, sample sizes, and other statistical properties. These graphical tools serve as aids in analyzing and investigating random variables. Exploring the properties and applications of these distributions requires more advanced mathematical knowledge, including concepts from probability theory and mathematical statistics.

From a code implementation perspective, these visualizations typically involve MATLAB's statistical functions (such as normpdf for normal distribution, exppdf for exponential distribution) combined with plotting functions like plot or fplot. The core algorithm involves calculating probability density values across a defined domain range and rendering smooth curves through interpolation techniques. Key implementation considerations include proper parameter configuration, optimal sampling point selection for accurate curve representation, and appropriate axis scaling to ensure visual clarity.