Introduction to Probability with Texas Holdem Examples illustrates both standard and advanced probability topics using the popular poker game of Texas Holdem, rather than the typical balls in urns. The author uses students natural interest in poker to teach important concepts in probability.
Probability Basics. Meaning of Probability. Basic Terminology. Axioms of Probability. Venn Diagrams. General Addition Rule. Counting Problems. Sample Spaces with Equally Probable Events. Multiplicative Counting Rule. Permutations. Combinations. Conditional Probability and Independence. Conditional Probability. Independence. Multiplication Rules. Bayes Rule and Structured Hand Analysis. Expected Value and Variance. Cumulative Distribution Function and Probability Mass Function. Expected Value. Pot Odds. Luck and Skill in Texas Holdem. Variance and Standard Deviation. Markov and Chebyshev Inequalities. Moment Generating Functions. Discrete Random Variables. Bernoulli Random Variables. Binomial Random Variables. Geometric Random Variables. Negative Binomial Random Variables. Poisson Random Variables. Continuous Random Variables. Probability Density Functions. Expected Value, Variance, and Standard Deviation. Uniform Random Variables Exponential Random Variables. Normal Random Variables. Pareto Random Variables. Continuous Prior and Posterior Distributions. Collections of Random Variables. Expected Value and Variance of Sums of Random Variables. Conditional Expectation Laws of Large Numbers and the Fundamental Theorem of Poker. Central Limit Theorem. Confidence Intervals for the Sample Mean. Random Walks. Simulation and Approximation Using Computers. Appendix A: Abbreviated Rules of Texas Holdem. Appendix B: Glossary of Poker Terms. Appendix C: Solutions to Selected Odd-Numbered Exercises. References and Suggested Reading. Index.
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