George G. Roussas's Introduction to Probability (2nd Edition) PDF

By George G. Roussas

ISBN-10: 0128001984

ISBN-13: 9780128001981

Publish 12 months note: First released in 2006
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Introduction to likelihood, moment Edition, is written for upper-level undergraduate scholars in records, arithmetic, engineering, machine technological know-how, operations examine, actuarial technology, organic sciences, economics, physics, and a few of the social sciences. together with his trademark readability and economic system of language, the writer explains vital thoughts of chance, whereas delivering precious workouts and examples of actual global functions for college kids to think about. After introducing primary likelihood innovations, the publication proceeds to subject matters together with targeted distributions, the joint chance density functionality, covariance and correlation coefficients of 2 random variables, and more.

• Demonstrates the applicability of likelihood to many human actions with examples and illustrations
• Discusses likelihood concept in a mathematically rigorous, but available way
• every one part presents appropriate proofs, and is via workouts and worthwhile hints
• solutions to even-numbered routines are supplied and exact solutions to all workouts can be found to teachers at the publication better half website

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Additional info for Introduction to Probability (2nd Edition)

Example text

4. B. V. Gnedenko, “Theory of Probability,” Chelsea, New York, 1962. 5. A. N. Kolmogorov, “Foundations of the Theory of Probability,” Chelsea, New York, 1956. 6. Marquis de Laplace, “A Philosophical Essay on Probabilities,” 1825 (English Translation), Dover, New York, 1951. 7. S. Ross, “A First Course in Probability,” Sixth Edition, Prentice Hall, New Jersey, 2002. 1. Random Variables It frequently occurs that in performing an experiment we are mainly interested in some functions of the outcome as opposed to the outcome itself.

The cumulative distribution function (cdf ) (or more simply the distribution function) F (·) of the random variable X is defined for any real number b, −∞ < b < ∞, by F (b) = P {X b} In words, F (b) denotes the probability that the random variable X takes on a value that is less than or equal to b. Some properties of the cdf F are (i) F (b) is a nondecreasing function of b, ∗ A set is countable if its elements can be put in a one-to-one correspondence with the sequence of positive integers. 2. Discrete Random Variables 27 (ii) limb→∞ F (b) = F (∞) = 1, (iii) limb→−∞ F (b) = F (−∞) = 0.

Random Variables It frequently occurs that in performing an experiment we are mainly interested in some functions of the outcome as opposed to the outcome itself. For instance, in tossing dice we are often interested in the sum of the two dice and are not really concerned about the actual outcome. That is, we may be interested in knowing that the sum is seven and not be concerned over whether the actual outcome was (1, 6) or (2, 5) or (3, 4) or (4, 3) or (5, 2) or (6, 1). These quantities of interest, or more formally, these real-valued functions defined on the sample space, are known as random variables.

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Introduction to Probability (2nd Edition) by George G. Roussas


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