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| Probability Models in Electrical and Computer Engineering | |
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| Mathematical models as tools in analysis and design | |
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| Deterministic models | |
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| Probability models | |
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| Statistical regularity | |
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| Properties of relative frequency | |
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| The axiomatic approach to a theory of probability | |
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| Building a probability model | |
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| A detailed example: a packet voice transmission system | |
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| Other examples | |
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| Communication over unreliable channels | |
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| Processing of random signals | |
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| Resource sharing systems | |
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| Reliability of systems | |
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| Overview of book | |
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| Summary | |
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| Problems | |
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| Basic Concepts of Probability Theory | |
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| Specifying random experiments | |
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| The sample space | |
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| Events | |
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| Set operations | |
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| The axioms of probability | |
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| Discrete sample spaces | |
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| Continuous sample spaces | |
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| Computing probabilities using counting methods | |
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| Sampling with replacement and with ordering | |
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| Sampling without replacement and with ordering | |
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| Permutations of n distinct objects | |
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| Sampling without replacement and without ordering | |
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| Sampling with replacement and without ordering | |
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| Conditional probability | |
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| Bayes' Rule | |
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| Independence of events | |
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| Sequential experiments | |
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| Sequences of independent experiments | |
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| The binomial probability law | |
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| The multinomial probability law | |
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| The geometric probability law | |
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| Sequences of dependent experiments | |
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| A computer method for synthesizing randomness: random number generators | |
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| Summary | |
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| Problems | |
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| Random Variables | |
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| The notion of a random variable | |
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| The cumulative distribution function | |
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| The three types of random variables | |
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| The probability density function | |
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| Conditional cdf's and pdf's | |
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| Some important random variables | |
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| Discrete random variables | |
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| Continuous random variables | |
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| Functions of a random variable | |
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| The expected value of random variables | |
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| The expected value of X. The expected value of Y = g(X). Variance of X | |
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| The Markov and Chebyshev | |