ANALYSIS OF PROBABILITY THEORY FOR STOCHASTIC PROCESSES AND RANDOMIZED ALGORITHMS

The analysis of probability theory as it relates to stochastic processes and randomised algorithms is presented in this work. It examines the foundational ideas of probability theory, such as random variables, probability distributions, and probability spaces. The research focuses on the characteristics and uses of stochastic processes, including Markov and Poisson processes. It also looks at how randomised algorithms for sorting, searching, optimisation, and graph algorithms are designed and analysed. In order to evaluate the behaviour and efficiency of stochastic processes and randomised algorithms, the study examines several important probabilistic approaches, including conditional expectation, moment generating functions, and probability inequalities. The theories and methods covered are illustrated through examples from the real world and case studies. In the context of stochastic processes and randomised algorithms, this research study offers a thorough analysis of probability theory. It highlights how crucial probability theory is for navigating ambiguity and coming to wise conclusions in uncertain and dynamic situations. The goal of the paper is to provide a useful resource for researchers, professionals, and students who are interested in stochastic processes, randomised algorithms, and probability theory