A first course in probability
This market-leading introduction to probability features exceptionally clear explanations of the mathematics of probability theory and explores its many diverse applications through numerous interesting and motivational examples. The outstanding problem sets are a hallmark feature of this book. Provides clear, complete explanations to fully explain mathematical concepts. Features subsections on the probabilistic method and the maximum-minimums identity. Includes many new examples relating to DNA matching, utility, finance, and applications of the probabilistic method. Features an intuitive treatment of probability--intuitive explanations follow many examples. The Probability Models Disk included with each copy of the book, contains six probability models that are referenced in the book and allow readers to quickly and easily perform calculations and simulations.
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approximation assume ball number ball selected binomial random variable black balls cards cent central limit theorem Chebyshev's inequality compute the probability conditional probability continuous random variable define denote the event denote the number desired probability dice discrete random variable Distributed Random Variables distributed with parameters E[Xt equal Equation 4.1 Example 2a Expectation Ch expected number fair coin Find the probability flips follows Hence identically distributed independent random variables independent trials joint probability large numbers law of large Let X denote nonnegative normal random variable normally distributed obtain occur P(EF player Poisson random variable possible outcomes prob Probability and Independence Probability Ch probability density function probability mass function problem proof Proposition 2.1 prove Random Variables Ch result sample space sequence Show Solution strong law Suppose Theoretical Exercises uniformly distributed urn contains variable with parameters white balls wins Xu X2 yields