Probabilistic Modeling for Conditional Statements

Abstract

A new mathematical framework is proposed in this study to comprehend the impact of program architecture on input random variables, the IF statement was the main topic. The primary idea that is theoretically and experimentally supported in this study is that the part of the joint pmf of a collection of random variables that represents the condition will be shifted to the part that represents the action. After sorting two random variables, the framework is used with four random variables, and the theoretically produced results were realistically validated. The study's equations can be applied to assessing probabilistic models of various sorting algorithms or other intricate program structures. This may also result in future investigations formalizing more precise execution time expectations.