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Lectures on Probability Theory and Mathematical Statistics

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Lectures on Probability Theory and Mathematical Statistics

4.85 68,469 ratings · 99,745 reviews
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Overview: This book is a collection of lectures on probability theory and mathematical statistics. It provides an accessible introduction to topics that are not usually found in elementary textbooks. It collects results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books.The main topics covered by the book are as follows.PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions.PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions.PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions.PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart.PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions.PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutski's Theorem.PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.

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Topics & Genres

Pages 656
Language En-US
Publisher CreateSpace Independent Publishing Platform
Published December 8, 2012
ISBN 17903816
Sponsored Content
Marco Taboga
About the Author
Marco Taboga
18,587 Followers

Marco Taboga is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, Marco Taboga enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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Donald  Davis
Donald Davis August 01, 2024
It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes.
Margaret Taylor
Margaret Taylor April 23, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Richard Anderson
Richard Anderson October 15, 2025
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Brian Torres
Brian Torres May 18, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Deborah Nguyen
Deborah Nguyen June 27, 2025
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
John Allen
John Allen September 15, 2025
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George Evans
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Donald Sanchez
Donald Sanchez August 30, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Karen Clark
Karen Clark July 15, 2025
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Betty Allen
Betty Allen November 27, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Kimberly Cruz
Kimberly Cruz April 03, 2025
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Mark Sanchez
Mark Sanchez June 21, 2025
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Mark Mitchell
Mark Mitchell March 09, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Gary Williams
Gary Williams September 22, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Linda Mitchell
Linda Mitchell November 21, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Richard Anderson
Richard Anderson January 30, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Elizabeth Collins
Elizabeth Collins March 16, 2025
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
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Jacob Smith June 22, 2024
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Steven Thomas
Steven Thomas May 18, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Andrew Diaz
Andrew Diaz December 21, 2025
It was adequate. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Kenneth Perez April 23, 2025
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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Betty Allen January 21, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Donna Hall
Donna Hall August 01, 2025
An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
David Hall
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Barbara Edwards
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A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Melissa Flores
Melissa Flores February 07, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Barbara Nelson
Barbara Nelson December 13, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Michael Collins
Michael Collins March 09, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Stephanie Wilson October 25, 2024
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Brian Johnson
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
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Karen Martinez July 19, 2025
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Jessica Gomez June 08, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Christopher Brown
Christopher Brown January 13, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Anthony Turner
Anthony Turner April 07, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Linda Robinson
Linda Robinson November 08, 2025
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
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Brian Clark December 15, 2025
An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. Unlikely to reread, but a reasonable expenditure of time.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Michelle Campbell June 23, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Mary Williams
Mary Williams April 06, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Eric Brown
Eric Brown October 28, 2025
It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Suitable if your reading queue is empty.
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Matthew King November 28, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Steven Parker June 09, 2025
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Sandra Nelson July 13, 2025
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Eric Rivera May 20, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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Anthony Johnson November 29, 2025
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
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Donald Sanchez November 20, 2025
I find myself somewhat conflicted. Certain acts were fascinating, while others felt like a slight endeavor to complete. A fair 3 stars.
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Dorothy Brown July 29, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Kenneth Nelson
Kenneth Nelson December 06, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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Lisa Martin October 12, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Kenneth Perez
Kenneth Perez February 28, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Amanda Green
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Brian Garcia
Brian Garcia May 06, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Donald Hernandez
Donald Hernandez March 20, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Steven Robinson
Steven Robinson March 16, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Karen Turner
Karen Turner July 25, 2025
I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Michelle Perez
Michelle Perez April 16, 2025
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
William Anderson
William Anderson February 20, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Kevin Brown
Kevin Brown August 16, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Barbara Turner
Barbara Turner May 25, 2025
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Richard Baker
Richard Baker October 10, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Andrew Baker
Andrew Baker January 01, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Barbara Gonzalez
Barbara Gonzalez December 09, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Brian Allen
Brian Allen August 06, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Jessica Roberts
Jessica Roberts November 09, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Margaret Smith
Margaret Smith May 24, 2024
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Sarah Nguyen
Sarah Nguyen June 02, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Sarah  Davis
Sarah Davis November 19, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Dorothy Clark
Dorothy Clark March 14, 2025
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
William Robinson
William Robinson November 23, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Barbara Nelson
Barbara Nelson January 28, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Anthony  Davis
Anthony Davis July 25, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Rebecca Gomez
Rebecca Gomez January 12, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Dorothy Rivera
Dorothy Rivera September 26, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Brian Clark
Brian Clark May 29, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Linda Robinson
Linda Robinson February 12, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Betty Gonzalez
Betty Gonzalez December 29, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Melissa Garcia
Melissa Garcia September 28, 2024
It was adequate. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
Sandra Moore
Sandra Moore February 24, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Melissa Lopez
Melissa Lopez December 17, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Eric Young
Eric Young January 22, 2024
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Sarah Taylor
Sarah Taylor February 03, 2024
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Brian Williams
Brian Williams November 29, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Betty Turner
Betty Turner January 06, 2025
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Susan Ramirez
Susan Ramirez June 26, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Ashley Mitchell
Ashley Mitchell April 29, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Jessica Edwards
Jessica Edwards April 10, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Christopher Baker
Christopher Baker January 30, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Karen Lewis
Karen Lewis April 22, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Michael Collins
Michael Collins March 09, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Emily Hill
Emily Hill March 07, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Christopher Brown
Christopher Brown March 28, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Michelle Perez
Michelle Perez September 21, 2025
It was adequate. Certain acts were fascinating, while others felt like a slight endeavor to complete. Unlikely to reread, but a reasonable expenditure of time.
Emily Taylor
Emily Taylor March 02, 2025
Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
David Thomas
David Thomas October 07, 2025
Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perhaps more aligned with a different audience's tastes.
Anthony Turner
Anthony Turner August 17, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
George Rodriguez
George Rodriguez January 12, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Sandra Moore
Sandra Moore June 26, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
George Sanchez
George Sanchez April 26, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Donald Anderson
Donald Anderson September 25, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Gary Jackson
Gary Jackson November 12, 2025
An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
Steven Thomas
Steven Thomas September 30, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Paul Baker
Paul Baker August 14, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Margaret Walker
Margaret Walker April 25, 2025
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Sandra Robinson
Sandra Robinson March 16, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Barbara Thomas
Barbara Thomas November 08, 2025
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Stephanie Carter
Stephanie Carter May 20, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Amanda Clark
Amanda Clark March 10, 2025
A decent, if standard, experience. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty.
Carol King
Carol King August 11, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Kimberly Cruz
Kimberly Cruz November 19, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Mark Sanchez
Mark Sanchez November 16, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Rebecca Martin
Rebecca Martin June 12, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Jessica Gomez
Jessica Gomez November 04, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
George Sanchez
George Sanchez March 24, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Michelle Wright
Michelle Wright February 18, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Cynthia Hernandez
Cynthia Hernandez August 14, 2025
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Mark Mitchell
Mark Mitchell January 13, 2024
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
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