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Description
Counterexamples in Probability: Third EditionMost mathematical examples illustrate the truth of a statement; conversely, counterexamples demonstrate a statement's falsity if changing the conditions. Mathematicians have always prized counterexamples as intrinsically enjoyable objects of study as well as valuable tools for teaching, learning, and research. This third edition of the definitive book on counterexamples in probability and stochastic processes presents the author's revisions and
Most mathematical examples illustrate the truth of a statement; conversely, counterexamples demonstrate a statement's falsity if changing the conditions. Mathematicians have always prized counterexamples as intrinsically enjoyable objects of study as well as valuable tools for teaching, learning, and research. This third edition of the definitive book on counterexamples in probability and stochastic processes presents the author's revisions and corrections in addition to a substantial new appendix.Suitable as a supplementary source for advanced undergraduates and graduate courses in the field of probability and stochastic processes, this volume features a wide variety of topics that are challenging in both content and detail. The text consists of four chapters and twenty-five sections. Each section begins with short introductory notes of basic definitions and main results. Counterexamples related to the main results follow, along with motivation for questions and counterstatements that range in difficulty. A familiarity with basic notions and results in probability and stochastic processes is assumed, and a chapter of supplementary remarks provides a wealth of information about original sources as well as references for further studies.
Binding Type: Paperback
Publisher: Dover Publications
Published: 01/15/2014
ISBN: 9780486499987
Pages: 400
Weight: 1.00lbs
Size: 8.40h x 5.50w x 1.00d
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★★★★★ 3
Too small for a lab retriever
Size: For Large & Medium dogs, Color: beige
If you have a large dog, I would not advise buying this item. It is very small. I was concerned about choking. My dog loved chewing on it and it is good quality, but I had to monitor constantly and tossed it the 2nd day due to choking fears. Great, if you have a smaller dog, but not good for lab retriever size!
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Reviewed in the United States on April 27, 2018
★★★★★ 1
fake fake fake
Size: For Large & Medium dogs, Color: beige, Size: For Large & Medium dogs, Color: beige
buyer beware. i don't know what this joke of a "dog toy" is but it's not what is pictured. no chance i'm giving this to my dog since i actually care about his well being. this product says that it's made in china, "patent pending" and that's its "safely tested in USA". also there's a weird stain on the inside of the packaging. no thank you, and i'm about ready to see the blood of whoever is behind potentially putting a dangerous toy in my dogs mouth. HELICOPTER DOG MOM COMING ATCHA
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Reviewed in the United States on April 3, 2017
★★★★★ 5
strong chew toy
Size: For Large & Medium dogs, Color: beige
great strong chew toy, keep my dog busy
smell strong but dog love it
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Reviewed in the United States on March 6, 2020
★★★★★ 5
Perfect for 5 Yorkies - they always go back to these...
Very durable and I'm always hearing my Yorkies gnawing and chewing on these... They really really like them. I've bought antlers and those plastic keys... But these win... The antlers are natural but I've learned they aren't healthy at all, and they still micro-splinter... The keys are too soft and plastic comes off.... These are perfect and I can see the plastic changing shape but not coming off. Perfect win. Oh, and being bright white I can see them in a dim or dark room so I don't step on them, my robot vacuum sees and avoids them, and I can see if my dogs have any bleeding gums, which they haven't had with these yet.
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Reviewed in the United States on January 9, 2023
★★★★★ 5
Super chewer loves these!
My super chewer loves these so much they are one of her favorite toys. She chews everything and these last forever
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Reviewed in the United States on November 8, 2023