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Description
Statistical Independence in Probability, Analysis and Number TheoryThis concise monograph in probability by Mark Kac, a well known mathematician, presumes a familiarity with Lebesgue's theory of measure and integration, the elementary theory of Fourier integrals, and the rudiments of number theory. Readers may then follow Dr. Kac's attempt "to rescue statistical independence from the fate of abstract oblivion by showing how in its simplest form it arises in various contexts cutting across different mathematical
This concise monograph in probability by Mark Kac, a well-known mathematician, presumes a familiarity with Lebesgue's theory of measure and integration, the elementary theory of Fourier integrals, and the rudiments of number theory. Readers may then follow Dr. Kac's attempt "to rescue statistical independence from the fate of abstract oblivion by showing how in its simplest form it arises in various contexts cutting across different mathematical disciplines."The treatment begins with an examination of a formula of Vieta that extends to the notion of statistical independence. Subsequent chapters explore laws of large numbers and mile Borel's concept of normal numbers; the normal law, as expressed by Abraham de Moivre and Andrey Markov's method; and number theoretic functions as well as the normal law in number theory. The final chapter ranges in scope from kinetic theory to continued fractions. All five chapters are enhanced by problems.
Binding Type: Paperback
Publisher: Dover Publications
Published: 08/15/2018
ISBN: 9780486821580
Pages: 112
Weight: 0.26lbs
Size: 8.00h x 5.00w x 0.30d
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★★★★★ 5
Great toy
Size: Large, Style: Squirrel
My two dogs loved to tear into this toy. Looks like the real thing. Not very loud squeek, so it works for me.
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Reviewed in the United States on December 31, 2025
★★★★★ 3
Falls apart fast
Size: Small, Style: Chipmunk
My yorkie had the "fur" shredded all over the place within an hour
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Reviewed in the United States on April 17, 2026
★★★★★ 5
Great toy!
Color: Blue
This is great and the dog loves it!
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Reviewed in the United States on April 30, 2026
★★★★★ 1
NOT for aggressive chewers.
Color: Blue, Color: Blue
Bruce had the stuffing out of this thing less than 5 minutes after handing it to him. This is not for aggressive chewers. Toys from the Dollar Tree have lasted longer than this thing. And now they want to charge me a buck to return it. I'll just let him finish shredding it. Maybe what's left will keep him entertained for a couple of hours.
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Reviewed in the United States on April 23, 2026
★★★★★ 5
loved it
Color: Blue
My pit mix LOVED this thing. We destuffed it and ripped an arm off but she still loves it
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Reviewed in the United States on March 6, 2026