A first course in probability
This market leader is written as an elementary introduction to the mathematical theory of probability for readers in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus. A major thrust of the Fifth Edition has been to make the book more accessible to today's readers. The exercise sets have been revised to include more simple, "mechanical" problems and new section of Self-test Problems, with fully worked out solutions, conclude each chapter. In addition many new applications have been added to demonstrate the importance of probability in real situations. A software diskette, packaged with each copy of the book, provides an easy to use tool to derive probabilities for binomial, Poisson, and normal random variables. It also illustrates and explores the central limit theorem, works with the strong law of large numbers, and more.
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assume Axioms of Probability ball number Bernoulli binomial random variable black balls cards central limit theorem Chebyshev's inequality Compute the probability conditional probability Consider continuous random variable define denote the event denote the number desired probability dice Distributed Random Variables distribution with parameters equal Equation Example 3a Expectation Ch expected number exponential random variable Find the probability flips follows Hence Independence Ch independent random variables independent trials joint density function joint probability Jointly Distributed Random large numbers law of large Let X denote normal random variable normally distributed number of successes obtain occur pair percent player Poisson random variable possible outcomes Probability and Independence probability density function probability mass function problem proof Proposition prove Random Variables Ch result sample space sequence Show Solution Suppose Theoretical Exercises uniformly distributed unit normal random urn contains variable with parameters white balls wins