Here\u2019s a list of some excellent resources across various formats\u2014books, YouTube channels, and blogs\u2014that cover advanced statistics and probability theories:<\/p>\n\n\n\n
Books:<\/strong><\/p>\n\n\n\n 1. “Introduction to Probability” by Dimitri P. Bertsekas and John N. Tsitsiklis<\/strong><\/p>\n\n\n\n – A comprehensive introduction to probability, available for free in PDF form on MIT’s OpenCourseWare.<\/p>\n\n\n\n – [Link to PDF](https:\/\/athenasc.com\/probbook.html<\/a>)<\/p>\n\n\n\n 2. “Think Stats” by Allen B. Downey<\/strong><\/p>\n\n\n\n – This book focuses on applying statistics to real-world data, with practical examples using Python.<\/p>\n\n\n\n – [Link to PDF](https:\/\/greenteapress.com\/wp\/think-stats-2e\/<\/a>)<\/p>\n\n\n\n 3. “The Elements of Statistical Learning” by Trevor Hastie, Robert Tibshirani, and Jerome Friedman<\/strong><\/p>\n\n\n\n – A highly regarded book on statistical learning, offering a deep dive into many advanced topics.<\/p>\n\n\n\n – [Link to PDF](https:\/\/web.stanford.edu\/~hastie\/ElemStatLearn\/<\/a>)<\/p>\n\n\n\n 4. “All of Statistics: A Concise Course in Statistical Inference” by Larry Wasserman<\/strong><\/p>\n\n\n\n – A great resource that covers both basic and advanced topics in statistics.<\/p>\n\n\n\n – [Link to PDF](https:\/\/www.stat.cmu.edu\/~larry\/all-of-statistics\/<\/a>)<\/p>\n\n\n\n 5. “Introduction to Statistical Thought” by Michael Lavine<\/strong><\/p>\n\n\n\n – This book covers the foundations of statistical inference and is available for free online.<\/p>\n\n\n\n – [Link to PDF](https:\/\/www.math.umass.edu\/~lavine\/Book\/book.html<\/a>)<\/p>\n\n\n\n YouTube Channels:<\/strong><\/p>\n\n\n\n 1. MIT OpenCourseWare – Probability and Statistics<\/strong><\/p>\n\n\n\n – Features lectures from MIT\u2019s undergraduate and graduate courses, including advanced topics in probability and statistics.<\/p>\n\n\n\n – [MIT OCW YouTube Channel](https:\/\/www.youtube.com\/user\/MIT<\/a>)<\/p>\n\n\n\n 2. Khan Academy<\/strong><\/p>\n\n\n\n – Although mostly known for basic statistics, Khan Academy also offers more advanced courses in probability and statistical inference.<\/p>\n\n\n\n – [Khan Academy – Probability & Statistics](https:\/\/www.youtube.com\/user\/khanacademy<\/a>)<\/p>\n\n\n\n 3. StatQuest with Josh Starmer<\/strong><\/p>\n\n\n\n – Excellent channel that breaks down complex statistical concepts into easily understandable segments, including advanced topics.<\/p>\n\n\n\n – [StatQuest YouTube Channel](https:\/\/www.youtube.com\/user\/joshstarmer<\/a>)<\/p>\n\n\n\n 4. Brilliant.org<\/strong><\/a><\/p>\n\n\n\n – While Brilliant offers paid content, their YouTube channel provides free videos covering advanced mathematical concepts, including probability and statistics.<\/p>\n\n\n\n – [Brilliant.org<\/a> YouTube Channel](https:\/\/www.youtube.com\/c\/Brilliantorg<\/a>)<\/p>\n\n\n\n 5. Harvard University – STAT110 (Probability)<\/strong><\/p>\n\n\n\n – Lectures from Harvard\u2019s popular STAT110 course, taught by Professor Joe Blitzstein, covering probability theory in depth.<\/p>\n\n\n\n – [Harvard University – STAT110 YouTube Channel](https:\/\/www.youtube.com\/playlist?list=PL2SOU6wwxB0v1kQTpqpuuGIjJRWJaFfeH<\/a>)<\/p>\n\n\n\n Blogs and Online Courses:<\/strong><\/p>\n\n\n\n 1. Cross Validated (Stack Exchange)<\/strong><\/p>\n\n\n\n – A Q&A site specifically for statistics, probability, and data science. It\u2019s a great place to see advanced problems discussed in depth.<\/p>\n\n\n\n – [Cross Validated](https:\/\/stats.stackexchange.com\/<\/a>)<\/p>\n\n\n\n 2. OpenIntro<\/strong><\/p>\n\n\n\n – Offers free textbooks, labs, and resources on statistics, including advanced topics.<\/p>\n\n\n\n – [OpenIntro](https:\/\/www.openintro.org\/<\/a>)<\/p>\n\n\n\n 3. Towards Data Science (Medium)<\/strong><\/p>\n\n\n\n – A popular blog on Medium with numerous articles on advanced statistics, probability, and their applications in data science.<\/p>\n\n\n\n – [Towards Data Science](https:\/\/towardsdatascience.com\/<\/a>)<\/p>\n\n\n\n 4. DataCamp Community<\/strong><\/p>\n\n\n\n – While DataCamp offers paid courses, their blog has free articles and tutorials on advanced statistical methods.<\/p>\n\n\n\n – [DataCamp Community](https:\/\/www.datacamp.com\/community<\/a>)<\/p>\n\n\n\n 5. Probability and Statistics EBook<\/strong><\/p>\n\n\n\n – An online resource that provides detailed explanations of advanced topics in probability and statistics.<\/p>\n\n\n\n – [Probability and Statistics EBook](http:\/\/www.probabilitycourse.com\/<\/a>)<\/p>\n\n\n\n MOOCs and Online Lectures:<\/strong><\/p>\n\n\n\n 1. Coursera – Statistical Learning by Stanford University<\/strong><\/p>\n\n\n\n – A free course that covers statistical learning, based on the book “The Elements of Statistical Learning.”<\/p>\n\n\n\n – [Coursera – Statistical Learning](https:\/\/www.coursera.org\/learn\/statistical-learning<\/a>)<\/p>\n\n\n\n 2. edX – Probability: The Science of Uncertainty and Data by MIT<\/strong><\/p>\n\n\n\n – A free course that dives deep into probability theory and applications.<\/p>\n\n\n\n – [edX – MIT Probability Course](https:\/\/www.edx.org\/course\/probability-the-science-of-uncertainty-and-data<\/a>)<\/p>\n\n\n\n 3. Harvard Online Learning – Data Science: Probability<\/strong><\/p>\n\n\n\n – Part of Harvard\u2019s Data Science Professional Certificate, this course is available for free auditing.<\/p>\n\n\n\n – [Harvard – Data Science: Probability](https:\/\/online-learning.harvard.edu\/course\/data-science-probability<\/a>)<\/p>\n\n\n\n These resources cover a broad range of advanced topics in probability and statistics, and they offer various levels of depth, from introductory overviews to rigorous academic treatments.<\/p>\n\n\n\n Here\u2019s a list of some excellent resources across various formats\u2014books, YouTube channels, and blogs\u2014that cover advanced statistics and probability theories: […]<\/p>\n","protected":false},"author":2,"featured_media":1300,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[389],"tags":[390,148],"class_list":["post-1299","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-statistics-and-probability","tag-probability","tag-statistics"],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2024\/08\/Stats.png?fit=1200%2C628&ssl=1","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7do02-kX","jetpack-related-posts":[{"id":1312,"url":"https:\/\/www.techandtrain.com\/blog\/2024\/10\/key-topics-for-random-processes-statistics-and-probability\/","url_meta":{"origin":1299,"position":0},"title":"Key Topics for Random Processes & Statistics and Probability","author":"Neil Harwani","date":"October 5, 2024","format":false,"excerpt":"Comprehensive List of Topics for Random Processes: 1. Stochastic Processes 2. Markov Chains 3. Continuous-Time Markov Chains 4. Markov Decision Processes (MDPs) 5. Random Walks 6. Poisson Processes 7. Renewal Processes 8. Stationary Processes 9. Weak and Strong Stationarity 10. Autocorrelation Function 11. Autoregressive Processes (AR) 12. Moving Average Processes\u2026","rel":"","context":"In "Random Processes"","block_context":{"text":"Random Processes","link":"https:\/\/www.techandtrain.com\/blog\/category\/random-processes\/"},"img":{"alt_text":"Credit: www.pixabay.com","src":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2024\/10\/Statistics.png?fit=1200%2C672&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2024\/10\/Statistics.png?fit=1200%2C672&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2024\/10\/Statistics.png?fit=1200%2C672&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2024\/10\/Statistics.png?fit=1200%2C672&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2024\/10\/Statistics.png?fit=1200%2C672&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":1426,"url":"https:\/\/www.techandtrain.com\/blog\/2025\/02\/top-100-mathematics-keywords-for-data-science-part-1\/","url_meta":{"origin":1299,"position":1},"title":"Top 100 mathematics keywords for Data Science – Part 1","author":"Neil Harwani","date":"February 22, 2025","format":false,"excerpt":"Whoever is teaching you data science without teaching you Mathematics especially optimization is not teaching it right to you. That's my biggest learning from Master of Data Science at IIT Gandhinagar - it will take you good 2 years to learn the related mathematics in all four major areas below.\u2026","rel":"","context":"In "Data Science"","block_context":{"text":"Data Science","link":"https:\/\/www.techandtrain.com\/blog\/category\/data-science\/"},"img":{"alt_text":"Image credit: www.Pixabay.com","src":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2025\/02\/Data.jpg?fit=1200%2C801&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2025\/02\/Data.jpg?fit=1200%2C801&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2025\/02\/Data.jpg?fit=1200%2C801&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2025\/02\/Data.jpg?fit=1200%2C801&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2025\/02\/Data.jpg?fit=1200%2C801&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":557,"url":"https:\/\/www.techandtrain.com\/blog\/2020\/02\/what-are-we-doing-in-ai-ml-data-science-decision-science-analytics-world-glossary\/","url_meta":{"origin":1299,"position":2},"title":"What are we doing in AI \/ ML \/ Data Science \/ Decision Science \/ Analytics World? – Glossary","author":"Neil Harwani","date":"February 17, 2020","format":false,"excerpt":"Over the last few years I have explored, programmed, worked in, researched and taught Data Science \/ AI \/ ML \/ Analytics \/ Decision Science to multiple students and with many software professionals. I have collected many keywords that you can google and explore. This will help you to keep\u2026","rel":"","context":"In "Analytics"","block_context":{"text":"Analytics","link":"https:\/\/www.techandtrain.com\/blog\/category\/analytics\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2020\/02\/Mathematics.jpg?fit=960%2C490&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2020\/02\/Mathematics.jpg?fit=960%2C490&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2020\/02\/Mathematics.jpg?fit=960%2C490&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2020\/02\/Mathematics.jpg?fit=960%2C490&ssl=1&resize=700%2C400 2x"},"classes":[]},{"id":698,"url":"https:\/\/www.techandtrain.com\/blog\/2021\/03\/four-waves-of-artificial-intelligence-machine-learning\/","url_meta":{"origin":1299,"position":3},"title":"Four waves of Artificial Intelligence & Machine Learning","author":"Neil Harwani","date":"March 19, 2021","format":false,"excerpt":"While teaching students in two different courses (AIML & \"Data Science and Analysis\"), there was a requirement to categorize historical AI & ML along with it's interface with Data Science. To start: AI is the superset, ML is a subset of AI, Neural Networks (Deep Learning) are specialized subsets of\u2026","rel":"","context":"In "Analytics"","block_context":{"text":"Analytics","link":"https:\/\/www.techandtrain.com\/blog\/category\/analytics\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2021\/03\/LighBulb.jpg?fit=1200%2C675&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2021\/03\/LighBulb.jpg?fit=1200%2C675&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2021\/03\/LighBulb.jpg?fit=1200%2C675&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2021\/03\/LighBulb.jpg?fit=1200%2C675&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2021\/03\/LighBulb.jpg?fit=1200%2C675&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":1288,"url":"https:\/\/www.techandtrain.com\/blog\/2024\/08\/learnings-from-emasters-data-science-for-decision-making-iit-gandhinagar-part-1\/","url_meta":{"origin":1299,"position":4},"title":"Learnings from eMasters Data Science for Decision Making – IIT Gandhinagar – Part 1","author":"Neil Harwani","date":"August 11, 2024","format":false,"excerpt":"Below are the learnings from eMasters Data Science for Decision Making - IIT Gandhinagar - Part 1. This needs to be an article in itself. You can find more details here about eDSDM here: e-Masters | IITGNX There is Mathematics for your AIML problem in feature engineering, preprocessing, evaluation metrics,\u2026","rel":"","context":"In "Analytics"","block_context":{"text":"Analytics","link":"https:\/\/www.techandtrain.com\/blog\/category\/analytics\/"},"img":{"alt_text":"Credits: www.Pixabay.com","src":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2024\/08\/DataScience.jpg?fit=1200%2C800&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2024\/08\/DataScience.jpg?fit=1200%2C800&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2024\/08\/DataScience.jpg?fit=1200%2C800&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2024\/08\/DataScience.jpg?fit=1200%2C800&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2024\/08\/DataScience.jpg?fit=1200%2C800&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":1074,"url":"https:\/\/www.techandtrain.com\/blog\/2023\/05\/short-list-of-good-courses-links-books-on-mathematics-operating-systems-and-aiml-chatgpt-part-1\/","url_meta":{"origin":1299,"position":5},"title":"Short list of good courses \/ links \/ books on Mathematics, Operating Systems and AIML \/ ChatGPT – Part 1","author":"Neil Harwani","date":"May 21, 2023","format":false,"excerpt":"Here is a short list of good courses \/ links \/ books on Mathematics, Operating Systems and AIML \/ ChatGPT - Part 1: Machine Learning Foundations: Linear Algebra Online Class | LinkedIn Learning, formerly Lynda.com Programming Foundations: Numerical Mathematics and Calculations Online Class | LinkedIn Learning, formerly Lynda.com Machine Learning\u2026","rel":"","context":"In "AIML"","block_context":{"text":"AIML","link":"https:\/\/www.techandtrain.com\/blog\/category\/aiml\/"},"img":{"alt_text":"Credits: www.Pixabay.com","src":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2023\/05\/geometry-g69584ea1e_1920.jpg?fit=1200%2C790&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2023\/05\/geometry-g69584ea1e_1920.jpg?fit=1200%2C790&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2023\/05\/geometry-g69584ea1e_1920.jpg?fit=1200%2C790&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2023\/05\/geometry-g69584ea1e_1920.jpg?fit=1200%2C790&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/www.techandtrain.com\/blog\/wp-content\/uploads\/2023\/05\/geometry-g69584ea1e_1920.jpg?fit=1200%2C790&ssl=1&resize=1050%2C600 3x"},"classes":[]}],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.techandtrain.com\/blog\/wp-json\/wp\/v2\/posts\/1299","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.techandtrain.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.techandtrain.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.techandtrain.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.techandtrain.com\/blog\/wp-json\/wp\/v2\/comments?post=1299"}],"version-history":[{"count":1,"href":"https:\/\/www.techandtrain.com\/blog\/wp-json\/wp\/v2\/posts\/1299\/revisions"}],"predecessor-version":[{"id":1301,"href":"https:\/\/www.techandtrain.com\/blog\/wp-json\/wp\/v2\/posts\/1299\/revisions\/1301"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.techandtrain.com\/blog\/wp-json\/wp\/v2\/media\/1300"}],"wp:attachment":[{"href":"https:\/\/www.techandtrain.com\/blog\/wp-json\/wp\/v2\/media?parent=1299"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.techandtrain.com\/blog\/wp-json\/wp\/v2\/categories?post=1299"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.techandtrain.com\/blog\/wp-json\/wp\/v2\/tags?post=1299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n