Step-by-Step Derivation and Simulation Verification in Mathematical Statistics // Provides step-by-step derivations of key results in mathematical statistics, including transformations of random variables, order statistics, and sampling distributions. The package combines analytical derivation with Monte Carlo simulation to compare theoretical and empirical results, facilitating deeper understanding of statistical theory and its computational implementation. The methods are motivated by standard treatments in mathematical statistics (Hogg, McKean, and Craig, 2019, ISBN: 9780134686991).