Probability, Statistics, And Random Processes For Electrical Engineering - Alberto Leon-Garcia

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Résumé :
This is the standard textbook for courses on probability and statistics, not substantially updated. While helping students to develop their problem-solving skills, the author motivates students with practical applications from various areas of ECE that demonstrate the relevance of probability theory to engineering practice. Included are chapter overviews, summaries, checklists of important terms, annotated references, and a wide selection of fully worked-out real-world examples. In this edition, the Computer Methods sections have been updated and substantially enhanced and new problems have been added....

Biographie:
unknown mean and known variance. Case 2: Xj's Gaussian...

Sommaire:

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 inequalities. Testing the fit of a distribution to data. Transform methods.

The characteristic function. The probability generating function. The laplace transform of the pdf.

Basic reliability calculations.

The failure rate function. Reliability of systems.

Computer methods for generating random variables.

The transformation method. The rejection method. Generation of functions of a random variable. Generating mixtures of random variables.

Entropy.

The entropy of a random variable. Entropy as a measure of information. The method of a maximum entropy.

Summary. Problems.

4. Multiple Random Variables.

Vector random variables.

Events and probabilities. Independence.

Pairs of random variables.

Pairs of discrete random variables. The joint cdf of X and Y. The joint pdf of two jointly continuous random variables. Random variables that differ in type.

Independence of two random variables. Conditional probability and conditional expectation.

Conditional probability. Conditional expectation.

Multiple random variables.

Joint distributions. Independence.

Functions of several random variables.

One function of several random variables. Transformation of random vectors. pdf of linear transformations. pdf of general transformations.

Expected value of functions of random variables.

The correlation and covariance of two random variables. Joint characteristic function.

Jointly Gaussian random variables.

n jointly Gaussian random variables. Linear transformation of Gaussian random variables. Joint characteristic function of Gaussian random variables.

Mean square estimation.

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