統(tǒng)計(jì)與隨機(jī)過程在信號(hào)處理中的應(yīng)用

內(nèi)容概要

The first editiofl of this book (1986) grew out of a set of notes used by the authorsto teach two one-semester courses on probability and random processes at Rensse-laer Polytechnic Institute (RPI). At that time the probability course at RPI was re-quired of all students in the Computer and Systems Engineering Program and was a highly recommended elective for students in closely related areas. While many un-dergraduate students took the course in the junior year, many seniors and first-year graduate students took the course for credit as well. Then, as now, most of the stu-dents were engineering students. To serve these students well, we felt that we should be rigorous in introducing fundamental principles while furnishing many op- portunities for students to develop their skills at solving problems.

書籍目錄

Introduction to Probability　1.1  INTRODUCTION:WHY STUDY PROBABILITY?　1.2  THE DIFFERENT KINDS OF PROBABILITY　　A. Probability as Intuition　　B. Probability as the Ratio of Favorable to Total Outcomes (Classical Theory)　　C. Probability as a Measure of Frequency of Occurrence　　D. Probability Based on an Axiomatic Theory　1.3  MISUSES,MISCALCULATIONS,AND PARADOXES 1N　PROBABILITY　1.4  SETS,FIELDS,AND EVENTS　Examples of Sample Spaces　1.5  AXIOMATIC DEFINITION OF PROBABILITY　1.6  JOINT, CONDITIONAL,AND TOTAL PROBABILITIES;INDEPENDENCE　1.7  BAYES' THEOREM AND APPLICATIONS　1.8  COMBINATORICS　　Occupancy Problems　　Extensions and Applications　1.9  BERNOULLI TRIALS--BINOMIAL AND MULTINOMIAL　　PROBABILITY LAWS　　Multinomial Probability Law　1.10    ASYMPTOTIC BEHAVIOR oF THE BINOMIAL LAW： THE POISSON LAW　1.11     NORMAL APPROXIMATION TO THE BINOMIAL LAW　1.12 SUMMARY    PROBLEMS    REFERENCES2　Random Variables  2.1     INTRODUCTION  2.2    DEFINITION OF A RANDOM VARIABLE  2.3    PROBABILITY DISTRIBUTION FUNCTION  2.4    PROBABILITY DENSITY FUNCTION(pdf) Four Other Common Density Functions More Advanced Density Functions  2.5  CONTINUOUS,DISCRETE,AND MIXED RANDOM VARIABLES　  Examples of Probability Mass Functions　2.6  CONDITIONAL AND JOINT DISTRIBUTIONS AND　　DENSITIES  2.7  FAILURE RATES  2.8  FUNCTIONS OF A RANDOM VARIABLE  2.9  SOLVING PROBLEMS OF THE TYPE  2.10  SOLVING PROBLEMS OF THE TYPE  2.11  SOLVING PROBLEMS OF THE TYPE W=h(X,Y)  2.12 SUMMARY    PROBLEMS    REFERENCES    ADDITIONAL READING3. Expectation and Introduction to Estimation  3.1  EXPECTED VALUE OF A RANDOM VARIABLE  On the Validity of Equation 3.1 -8　3.2   CONDITIONAL EXPECTATIONS　　Conditional Expectation as a Random Variable……

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