Course Contents
Probability: Random experiments, sample space, events, axiomatic definition of probability, probability spaces, properties of probability measure, probability of union of events, conditional probability, Bayes theorem, independence of events.
Random variables and Random Vectors: Random variables, distribution functions, probability mass function (pmf) of discrete random variables, probability density function (pdf) of continuous random variables, random vector, marginal and conditional distributions for two jointly distributed random variables, independence of random variables, mathematical expectation, moments, factorial moments, moment generating function, probability generating function.
Statistical distributions: Discrete uniform distribution, Bernoulli distribution, binomial distribution, Poisson distribution, geometric distribution, negative binomial distribution, hyper-geometric distribution, Continuous uniform distribution, normal distribution, error function, exponential distribution, reliability function and instantaneous failure rate for exponential distribution, Cauchy distribution, Chebyshev’s inequality, Central limit theorem.
Statistical Methods: Measures of central tendency, dispersion, simple linear regression, method of least squares, correlation coefficient, rank correlation, correlation ratio.
Queuing Theory and network models: Basic elements of queuing models, queue discipline, pure birth and death models, M/M/1 queuing model, Distribution of number of arrivals and inter arrival time, steady state probability distribution, M/M/c queuing model.
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