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I
Introduction: Sample space, Events, Algebra of events, Bayes' Rule,
Bernoulli Trials. Probability Distribution and Probability Densities:
Bernoulli, Binomial, Poisson, Normal, rectangular and exponential
distributions and their PDFs. Moments and MGFs for above distributions.
II Discrete Random Variables: Random Variables and their event
space, probability mass function. Distribution Functions. Probability
Generating Function. Expectations: Moments, Computation of mean Time to
failure. Bernoulli & Poisson Processes.
III Queuing Theory: Pure birth, Pure Death and Birth-Death
Processes, mathematical Models for M/M/I, M/M/N, M/M/S and M/M/S/N/
queues.
IV Discrete Parameter Markov Chains: M/G/I Queuing Model, Discrete
Parameter Birth-Death Process.
V Network of queues: Open Queuing Networks. Correlation &
Regression: Linear regression, Method of least squares, Normal regression
and correlation Analysis.
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