Probability, Statistics, and Random Processes For Electrical Engineering

1. Probability Models in Electrical and Computer Engineering. Mathematical models as tools in analysis and design. Deterministic models. Probability models. Statistical regularity. Properties of relative frequency. The axiomatic approach to a theory of probability. Building a probability model. A detailed example: a packet voice transmission system. Other examples. Communication over unreliable channels. Processing of random signals. Resource sharing systems. Reliability of systems. Overview of book. Summary. Problems. 2. Basic Concepts of Probability Theory. Specifying random experiments. The sample space. Events. Set operations. The axioms of probability. Discrete sample spaces. Continuous sample spaces. Computing probabilities using counting methods. Sampling with replacement and with ordering. Sampling without replacement and with ordering. Permutations of n distinct objects. Sampling without replacement and without ordering. Sampling with replacement and without ordering. Conditional probability. Bayes' Rule. Independence of events. Sequential experiments. Sequences of independent experiments. The binomial probability law. The multinomial probability law. The geometric probability law. Sequences of dependent experiments. A computer method for synthesizing randomness: random number generators. Summary. Problems. 3. Random Variables. The notion of a random variable. The cumulative distribution function. The three types of random variables. The probability density function. Conditional cdf's and pdf's. Some important random variables. Discrete random variables. Continuous random variables. Functions of a random variable. The expected value of random variables. The expected value of X. The expected value of Y = g(X). Variance of X. The Markov and Chebyshev