Traditionally, computer simulation techniques are used to perform
probabilistic analysis. However, they provide less accurate results
and cannot handle large-scale problems due to their enormous CPU
time requirements. Recently, a significant amount of formalization
has been done in higher-order logic that allows us to conduct
precise probabilistic analysis using theorem proving and thus
overcome the limitations of the simulation based probabilistic
analysis approach. Some major contributions include the
formalization of both discrete and continuous random variables and
the verification of corresponding probabilistic and statistical
properties. This book presents a concise description of the
infrastructures behind these capabilities and their utilization to
conduct the probabilistic analysis of real-world systems. The case
studies of the round-off error of a digital processor, the Coupon
Collector's problem and the Stop-and-Wait protocol are used to
illustrate the proposed analysis approach. Designed as an
independent research tool, the book presents a well-thought-out
treatment of a rapidly emerging multidisciplinary field across
Mathematics, Computer Science and Engineering.
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