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Introduction to Probability and Its Applications

ISBN: 9780534237905 | 0534237908
Edition: 2nd
Format: Hardcover
Publisher: Cengage Learning
Pub. Date: 11/18/1994

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SummaryTable of Contents
In this calculus-based text, theory is developed to a practical degree around models used in real-world applications. Proofs of theorems and "tricky" probability calculations are minimized. Computing and simulation are introduced to make more difficult problems accessible (although the material does not depend on the computer for continuity).
Introduction to Probability and its Applications provides a solid and straightforward one-semester introduction to probability, focusing on the subject's utility in solving re... MORE
Probability in the World Around Us
1(5)
Why Study Probability?
1(1)
Deterministic and Probabilistic Models
... MORE		2(1)
Applications of Probability
3(2)
A Brief Historical Note
5(1)
A Look Ahead
5(1)
Probability
6(61)
Understanding Randomness: An Intuitive Notion of Probability
6(3)
A Brief Review of Set Notation
9(4)
Definition of Probability
13(8)
Counting Rules Useful in Probability
21(11)
Conditional Probability and Independence
32(8)
Rules of Probability
40(17)
Odds, Odds Ratios, and Relative Risk
57(3)
Activities for Students: Simulation
60(2)
Summary
62(5)
Supplementary Exercises
62(5)
Discrete Probability-Distributions
67(71)
Random Variables and Their Probability Distributions
67(6)
Expected Values of Random Variables
73(13)
The Bernoulli Distribution
86(1)
The Binomial Distribution
87(10)
The Geometric Distribution
97(3)
The Negative Binomial Distribution
100(4)
The Poisson Distribution
104(5)
The Hypergeometric Distribution
109(6)
The Moment-Generating Function
115(2)
The Probability-generating Function
117(3)
Markov Chains
120(8)
Activities for Students: Simulation
128(5)
Summary
133(5)
Supplementary Exercises
134(4)
Continuous Probability Distributions
138(85)
Continuous Random Variables and Their Probability Distributions
138(8)
Expected Values of Continuous Random Variables
146(5)
The Uniform Distribution
151(5)
The Exponential Distribution
156(6)
The Gamma Distribution
162(5)
The Normal Distribution
167(21)
The Beta Distribution
188(4)
The Weibull Distribution
192(6)
Reliability
198(4)
Moment-generating Functions for Continuous Random Variables
202(4)
Expectations of Discontinuous Functions and Mixed Probability Distributions
206(5)
Activities for Students: Simulation
211(7)
Summary
218(5)
Supplementary Exercises
218(5)
Multivariate Probability Distributions
223(46)
Bivariate and Marginal Probability Distributions
223(9)
Conditional Probability Distributions
232(3)
Independent Random Variables
235(4)
Expected Values of Functions of Random Variables
239(11)
The Multinomial Distribution
250(5)
More on the Moment-generating Function
255(2)
Conditional Expectations
257(4)
Compounding and Its Applications
261(1)
Summary
262(7)
Supplementary Exercises
263(6)
Functions of Random Variables
269(33)
Introduction
269(1)
Method of Distribution Functions
270(6)
Method of Transformations
276(5)
Method of Conditioning
281(2)
Method of Moment-generating Functions
283(6)
Order Statistics
289(6)
Probability-generating Functions: Applications to Random Sums of Random Variables
295(3)
Summary
298(4)
Supplementary Exercises
298(4)
Some Approximations to Probability Distributions: Limit Theorems
302(25)
Introduction
302(1)
Convergence in Probability
302(4)
Convergence in Distribution
306(5)
The Central Limit Theorem
311(13)
Combination of Convergence in Probability and Convergence in Distribution
324(1)
Summary
325(2)
Supplementary Exercises
325(2)
Extended Applications of Probability
327(15)
The Poisson Process
327(3)
Birth and Death Processes: Biological Applications
330(2)
Queues: Engineering Applications
332(1)
Arrival Times for the Poisson Process
333(1)
Infinite Server Queue
334(2)
Renewal Theory: Reliability Applications
336(3)
Summary
339(3)
Exercises
340(2)
Appendix Tables342(11)
Notes on Computer Simulations353(2)
References355(2)
Answers to Selected Exercises357(16)
Index373

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