Suppose that N is a Z+-valued random variable and that X,X1, X2, . . . is a sequence of independent and identically distributed Z+ random variables independent of N . In this paper we are interested in properties of the conditional variable Nk D =(N | ∑Nj=1 Xj = k). In particular, we want to know the asymptotic behavior of the conditional mean ENk or the conditional variance var Nk as k → ∞. We...

We apply the known formulae of the RESTART problem to Markov models of software (and many other) systems, and derive new equations. We show how checkpoints might be included, with their resultant performance under RESTART. The result is a complete procedure for finding the mean, variance, and tail behavior of the job completion time as a function of the failure rate. We also provide a detailed ...

During the last two decades, new models were developed in actuarial sciences. Different notions of insurance company ruin (bankruptcy) and other objective functions evaluating performance introduced. Several types decision (such as dividend payment, reinsurance, investment) are used for optimization functioning. Therefore, it is necessary to ensure that model under consideration stable with res...

In many domains, risk assessment is a defined methodology aimed at determining and quantifying risks associated with a specific activity, including the identification and characterization of potential hazards and their probability of occurrence. It relies on the gathering and interpretation of scientific and technical data and must be carried out in a scientifically sound and transparent manner...

Several prominent educational institutions have recently increased their use of team-based projects to both enhance learning and aid in assessment. We present some of our ongoing research into the use of project-based learning for the instruction of applied probability and stochastic processes at the high school, undergraduate, and graduate levels. In particular, we will demonstrate how “real-w...