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Discrete Event Simulation
Overview of basic concepts from probability and statistics concerning
random variables, correlation, estimation, confidence intervals,
hypothesis testing. Generation and testing of random numbers. Generation
of random variates, random vectors, correlated random variates and
stochastic processes. Input modeling; useful probability distributions;
hypothesizing families of distributions, estimation of parameters, testing
goodness of fit. Simulation Output data analysis for a single system;
statistical analyses for transient systems and systems in statistical
equilibrium. Comparing alternative system configurations; confidence
intervals, ranking and selection. Variance reduction techniques.
Experimental design, sensitivity analysis and optimization.

Theory of Estimation:
Population and samples; Parametric and non-parametric models; Exponential
and location-scale families; Sufficiency and minimal sufficiency; Complete
statistics; Unbiased and UMVU estimation; Asymptotically unbiased
estimators; Method of moments; Bayes estimators; Invariance; admissibility
of Bayes rule; Minmax Theorem Maximum Likelihood Estimation. Consistency
and efficiency. UMVU estimators and their properties. Application to
normal and exponential one and two sample problems. Information inequality
(multiple parameter case).