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An Introduction to Probability


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Table of Contents

I. Randomness.- 2. Probability.- 3. Independent Events.- 4. Conditional Probability.- 5. Bayes' Theorem.- 6. Review of Randomness.
Part II Discrete Random Variables7. Discrete Versus Continuous Random Variables.- 8.- Probability Mass Functions and CDFs.- 9. Independence and Conditioning.- 10. Expected Values of Discrete Random Variables.- 11. Expected Values of Sums of Random Variables.- 12. Variance of Discrete Random Variables.- 13. Review of Discrete Random Variables.
Part III Named Discrete Random Variables 14.- Bernoulli Random Variables.- 15. Binomial Random Variables.- 16. Geometric Random Variables.- 17.Negative Binomial Random Variables.- 18. Poisson Random Variables.- 19. Hypergeometric Random Variables.- 20. Discrete Uniform Random Variables.- 21. Review of Named Discrete Random Variables.
Part IV Counting
22. Introduction to Counting.- 23. Two Case Studies in Counting.

Part V Continuous Random Variables24. Continuous Random Variables and PDFs.- 25. Joint Densities.- 26. Independent Continuous Random Variables.- 27. Conditional Distributions.- 28. Expected Values of Continuous Random Variables.- 29. Variance of Continuous Random Variables.- 30. Review of Continuous Random Variables
Part VI Named Continuous Random Variables 31. Continuous Uniform Random Variables.- 32. Exponential Random Variables.- 33. Gamma Random Variables.- 34. Beta Random Variables.- 35. Normal Random Variables.- 36. Sums of Independent Normal Random Variables.- 37. Central Limit Theorem
Part VII Additional Topics39. Variance of Sums; Covariance; Correlation.- 40. Conditional Expectation.- 41. Markov and Chebyshev Inequalities.- 42. Order Statistics.- 43. Moment Generating Functions.- 44.

About the Author

Mark Daniel Ward is an Associate Professor of Statistics at Purdue University. Dr. Ward is currently the Principal Investigator for the NSF grant "MCTP: Sophomore Transitions: Bridges into a Statistics Major and Big Data Research Experiences via Learning Communities". He is also an Associate Director of the Center for Science of Information.

Ellen Gundlach has been teaching introductory statistics and probability classes at Purdue University as a continuing lecturer since 2002. She is an associate editor of CAUSEweb and editor of the MERLOT Statistics Board. Her research interests include K12 outreach activities and online and hybrid teaching.

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