A guide to simulation (2nd ed.)
A guide to simulation (2nd ed.)
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
ML For the Working Programmer
A stochastic process on the hypercube with applications to peer-to-peer networks
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Modern Cryptography: Theory and Practice
Modern Cryptography: Theory and Practice
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Communication Networks: Fundamental Concepts and Key Architectures
Communication Networks: Fundamental Concepts and Key Architectures
VESTA: A Statistical Model-checker and Analyzer for Probabilistic Systems
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Probabilistic guarded commands mechanized in HOL
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
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
Verification of expectation properties for discrete random variables in HOL
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Optimal cover time for a graph-based coupon collector process
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Quantitative temporal logic mechanized in HOL
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Proofs of randomized algorithms in CoQ
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Formal probabilistic analysis: a higher-order logic based approach
ABZ'10 Proceedings of the Second international conference on Abstract State Machines, Alloy, B and Z
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Statistical quantities, such as expectation (mean) and variance, play a vital role in the present age probabilistic analysis. In this paper, we present some formalization of expectation theory that can be used to verify the expectation and variance characteristics of discrete random variables within the HOL theorem prover. The motivation behind this is the ability to perform error free probabilistic analysis, which in turn can be very useful for the performance and reliability analysis of systems used in safety-critical domains, such as space travel, medicine and military. We first present a formal definition of expectation of a function of a discrete random variable. Building upon this definition, we formalize the mathematical concept of variance and verify some classical properties of expectation and variance in HOL. We then utilize these formal definitions to verify the expectation and variance characteristics of the Geometric random variable. In order to demonstrate the practical effectiveness of the formalization presented in this paper, we also present the probabilistic analysis of the Coupon Collector's problem in HOL.