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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AXIOMS OF PROBABILITY
CONDITIONAL PROBABILITY AND INDEPENDENCE
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approximately assume ball number Bernoulli binomial random variable black balls cards central limit theorem Chebyshev's inequality components compute conditional probability Consider continuous random variable defined denote the event denote the number desired probability dice discrete random variable distribution function distribution with parameters equal Equation Example expected number expected value exponential random variable Find the probability flips follows given Hence hint identically distributed independent trials inequality joint density function joint probability large numbers least Let X denote nonnegative normal random variable normally distributed number of successes obtain occur pair percent permutation player Poisson random variable preceding prob probability density function probability mass function problem Proposition random number random vari randomly chosen result sample space sequence Show simulate Solution Let Suppose tion total number uniform 0,1 uniformly distributed Var(A variable with mean variable with parameters white balls wins yields