Leseprobe
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The Probability Lifesaver
Steven J. Miller
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
The essential lifesaver for students who want to master probability
For students learning probability, its numerous applications, techniques, and methods can seem intimidating and overwhelming. That's where The Probability Lifesaver steps in. Designed to serve as a complete stand-alone introduction to the subject or as a supplement for a course, this accessible and user-friendly study guide helps students comfortably navigate probability's terrain and achieve positive results.
The Probability Lifesaver is based on a successful course that Steven Miller has taught at Brown University, Mount Holyoke College, and Williams College. With a relaxed and informal style, Miller presents the math with thorough reviews of prerequisite materials, worked-out problems of varying difficulty, and proofs. He explores a topic first to build intuition, and only after that does he dive into technical details. Coverage of topics is comprehensive, and materials are repeated for reinforcement—both in the guide and on the book's website. An appendix goes over proof techniques, and video lectures of the course are available online. Students using this book should have some familiarity with algebra and precalculus.
The Probability Lifesaver not only enables students to survive probability but also to achieve mastery of the subject for use in future courses.
- A helpful introduction to probability or a perfect supplement for a course
- Numerous worked-out examples
- Lectures based on the chapters are available free online
- Intuition of problems emphasized first, then technical proofs given
- Appendixes review proof techniques
- Relaxed, conversational approach
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Probability distribution, Exact test, Random element, Probability, Free parameter, Markov's inequality, Cantor's diagonal argument, Rate of convergence, Dummy variable (statistics), Null hypothesis, Scientific notation, Sign (mathematics), Mutual exclusivity, Normal distribution, Significant figures, False positive rate, Law of large numbers, Root test, Type I and type II errors, Summation, Central limit theorem, Z-test, Expected value, Gamma function, Arbitrarily large, Benford's law, Analytic proof, Geometric distribution, Travelling salesman problem, Negative binomial distribution, Probability-generating function, Series expansion, Calculation, Chebyshev's inequality, One-Tailed Test, Infimum and supremum, Student's t-test, Accuracy and precision, Random sequence, Weighted arithmetic mean, Moment-generating function, Poisson distribution, Variance, Wrong direction, Disjoint union, Random variable, Greedy algorithm, Binomial distribution, Convolution, Counting, Chi-squared test, Divisibility rule, Berry–Esseen theorem, Double counting (proof technique), Commutative property, Pigeonhole principle, Fair coin, Lucky number, Inclusion–exclusion principle, Almost surely, Floor and ceiling functions, Test statistic, Continuum hypothesis, Bernoulli trial, Extended real number line, P-value, Chi-squared distribution, Special case, New Math, Ratio test