Modern Cryptography: Theory and Practice
Modern Cryptography: Theory and Practice
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
VESTA: A Statistical Model-checker and Analyzer for Probabilistic Systems
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Quantitative Analysis With the Probabilistic Model Checker PRISM
Electronic Notes in Theoretical Computer Science (ENTCS)
Verification of probabilistic properties in HOL using the cumulative distribution function
IFM'07 Proceedings of the 6th international conference on Integrated formal methods
Formalized Information-Theoretic Proofs of Privacy Using the HOL4 Theorem-Prover
PETS '08 Proceedings of the 8th international symposium on Privacy Enhancing Technologies
Using Theorem Proving to Verify Expectation and Variance for Discrete Random Variables
Journal of Automated Reasoning
Performance Analysis and Functional Verification of the Stop-and-Wait Protocol in HOL
Journal of Automated Reasoning
Formal Probabilistic Analysis of Stuck-at Faults in Reconfigurable Memory Arrays
IFM '09 Proceedings of the 7th International Conference on Integrated Formal Methods
Formalization of Measure Theory and Lebesgue Integration for Probabilistic Analysis in HOL
ACM Transactions on Embedded Computing Systems (TECS) - Special Issue on Modeling and Verification of Discrete Event Systems
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One of the most important concepts in probability theory is that of the expectation of a random variable, which basically summarizes the distribution of the random variable in a single number. In this paper, we develop the basic techniques for analyzing the expected values of discrete random variables in the HOL theorem prover. We first present a formalization of the expectation function for discrete random variables and based on this definition, the expectation properties of three commonly used discrete random variables are verified. Then, we utilize the definition of expectation in HOL to verify the linearity of expectation property, a useful characteristic to analyze the expected values of probabilistic systems involving multiple random variables. To demonstrate the usefulness of our approach, we verify the expected value of the Coupon Collector's problem within the HOL theorem prover.