{"id":2183,"date":"2019-05-24T06:36:57","date_gmt":"2019-05-24T06:36:57","guid":{"rendered":"https:\/\/www.aiproblog.com\/index.php\/2019\/05\/24\/free-textbook-probability-course-harvard-university-based-on-r\/"},"modified":"2019-05-24T06:36:57","modified_gmt":"2019-05-24T06:36:57","slug":"free-textbook-probability-course-harvard-university-based-on-r","status":"publish","type":"post","link":"https:\/\/www.aiproblog.com\/index.php\/2019\/05\/24\/free-textbook-probability-course-harvard-university-based-on-r\/","title":{"rendered":"Free Textbook: Probability Course, Harvard University (Based on R)"},"content":{"rendered":"<p>Author: Capri Granville<\/p>\n<div>\n<p>A free online version of the second edition of the book based on Stat 110,\u00a0<em>Introduction to Probability<\/em>\u00a0by Joe Blitzstein and Jessica Hwang,\u00a0is now available <a href=\"http:\/\/probabilitybook.net\/\" target=\"_blank\" rel=\"noopener noreferrer\">here<\/a>.\u00a0Print copies are available via\u00a0<a href=\"https:\/\/www.crcpress.com\/Introduction-to-Probability-Second-Edition\/Blitzstein-Hwang\/p\/book\/9781138369917\" title=\"\">CRC Press<\/a>,<span>\u00a0<\/span><a href=\"https:\/\/amzn.to\/2Ubh7D8\" title=\"\">Amazon<\/a>, and elsewhere.\u00a0 Stat110x is also available as an free edX course, <a href=\"https:\/\/www.edx.org\/course\/introduction-to-probability-0\" target=\"_blank\" rel=\"noopener noreferrer\">here<\/a>.\u00a0<\/p>\n<p>The edX course focuses on animations, interactive features, readings, and problem-solving, and\u00a0is<span>\u00a0<\/span><strong>complementary<\/strong><span>\u00a0<\/span>to the Stat 110 lecture videos on YouTube, which are available <a href=\"https:\/\/goo.gl\/i7njSb\" target=\"_blank\" rel=\"noopener noreferrer\">here<\/a>.\u00a0The Stat110x animations are available within the course and <a href=\"https:\/\/goo.gl\/g7pqTo\" target=\"_blank\" rel=\"noopener noreferrer\">here<\/a>. For more information, visit <a href=\"https:\/\/projects.iq.harvard.edu\/stat110\" target=\"_blank\" rel=\"noopener noreferrer\">Stat110 at Harvard<\/a>. A 10-page cheat sheet summarizing the content, is available <a href=\"https:\/\/www.datasciencecentral.com\/profiles\/blogs\/probability-cheat-sheet\" target=\"_blank\" rel=\"noopener noreferrer\">here<\/a>. For more free books, <a href=\"https:\/\/www.datasciencecentral.com\/profiles\/blogs\/new-books-and-resources-for-dsc-members\" target=\"_blank\" rel=\"noopener noreferrer\">visit this page<\/a>.\u00a0<\/p>\n<\/p>\n<p><a href=\"https:\/\/storage.ning.com\/topology\/rest\/1.0\/file\/get\/2661275427?profile=original\" target=\"_blank\" rel=\"noopener noreferrer\"><img decoding=\"async\" src=\"https:\/\/storage.ning.com\/topology\/rest\/1.0\/file\/get\/2661275427?profile=RESIZE_710x\" class=\"align-center\"><\/a><\/p>\n<p><span style=\"font-size: 14pt;\"><strong>Table of Contents<\/strong><\/span><\/p>\n<p><strong>1. Probability and Counting<\/strong><\/p>\n<ul>\n<li>Why study probability?<\/li>\n<li>Sample spaces and Pebble World<\/li>\n<li>Naive definition of probability<\/li>\n<li>How to count<\/li>\n<li>Story proofs<\/li>\n<li>Non-naive definition of probability<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p><strong>2. Conditional Probability<\/strong><\/p>\n<ul>\n<li>The importance of thinking conditionally<\/li>\n<li>Definition and intuition<\/li>\n<li>Bayes&#8217; rule and the law of total probability<\/li>\n<li>Conditional probabilities are probabilities<\/li>\n<li>Independence of events<\/li>\n<li>Coherency of Bayes&#8217; rule<\/li>\n<li>Conditioning as a problem-solving tool<\/li>\n<li>Pitfalls and paradoxes<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p><strong>3. Random Variables and Their Distributions<\/strong><\/p>\n<ul>\n<li>Random variables<\/li>\n<li>Distributions and probability mass functions<\/li>\n<li>Bernoulli and Binomial<\/li>\n<li>Hypergeometric<\/li>\n<li>Discrete Uniform<\/li>\n<li>Cumulative distribution functions<\/li>\n<li>Functions of random variables<\/li>\n<li>Independence of rvs<\/li>\n<li>Connections between Binomial and Hypergeometric<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p><strong>4. Expectation<\/strong><\/p>\n<ul>\n<li>Definition of expectation<\/li>\n<li>Linearity of expectation<\/li>\n<li>Geometric and Negative Binomial<\/li>\n<li>Indicator rvs and the fundamental bridge<\/li>\n<li>Law of the unconscious statistician (LOTUS)<\/li>\n<li>Variance<\/li>\n<li>Poisson<\/li>\n<li>Connections between Poisson and Binomial<\/li>\n<li>*Using probability and expectation to prove existence<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p><strong>5. Continuous Random Variables<\/strong><\/p>\n<ul>\n<li>Probability density functions<\/li>\n<li>Uniform<\/li>\n<li>Universality of the Uniform<\/li>\n<li>Normal<\/li>\n<li>Exponential<\/li>\n<li>Poisson processes<\/li>\n<li>Symmetry of iid continuous rvs<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p><strong>6. Moments<\/strong><\/p>\n<ul>\n<li>Summaries of a distribution<\/li>\n<li>Interpreting moments<\/li>\n<li>Sample moments<\/li>\n<li>Moment generating functions<\/li>\n<li>Generating moments with MGFs<\/li>\n<li>Sums of independent rvs via MGFs<\/li>\n<li>*Probability generating functions<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p><strong>7. Joint Distributions<\/strong><\/p>\n<ul>\n<li>Joint, marginal, and conditional<\/li>\n<li>D LOTUS<\/li>\n<li>Covariance and correlation<\/li>\n<li>Multinomial<\/li>\n<li>Multivariate Normal<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p><strong>8. Transformations<\/strong><\/p>\n<ul>\n<li>Change of variables<\/li>\n<li>Convolutions<\/li>\n<li>Beta<\/li>\n<li>Gamma<\/li>\n<li>Beta-Gamma connections<\/li>\n<li>Order statistics<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p><strong>9. Conditional Expectation<\/strong><\/p>\n<ul>\n<li>Conditional expectation given an event<\/li>\n<li>Conditional expectation given an rv<\/li>\n<li>Properties of conditional expectation<\/li>\n<li>*Geometric interpretation of conditional expectation<\/li>\n<li>Conditional variance<\/li>\n<li>Adam and Eve examples<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p>10. Inequalities and Limit Theorems<\/p>\n<p>Inequalities<\/p>\n<p>Law of large numbers<\/p>\n<p>Central limit theorem<\/p>\n<p>Chi-Square and Student-t<\/p>\n<p>Recap<\/p>\n<p>R<\/p>\n<p>Exercises<\/p>\n<p><strong>11. Markov Chains<\/strong><\/p>\n<ul>\n<li>Markov property and transition matrix<\/li>\n<li>Classification of states<\/li>\n<li>Stationary distribution<\/li>\n<li>Reversibility<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p><strong>12. Markov Chain Monte Carlo<\/strong><\/p>\n<ul>\n<li>Metropolis-Hastings<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p><strong>13. Poisson Processes<\/strong><\/p>\n<ul>\n<li>Poisson processes in one dimension<\/li>\n<li>Conditioning, superposition, thinning<\/li>\n<li>Poisson processes in multiple dimensions<\/li>\n<li>Recap<\/li>\n<li>R<\/li>\n<li>Exercises<\/li>\n<\/ul>\n<p><strong>A Math<\/strong><\/p>\n<ul>\n<li>Sets<\/li>\n<li>Functions<\/li>\n<li>Matrices<\/li>\n<li>Difference equations<\/li>\n<li>Differential equations<\/li>\n<li>Partial derivatives<\/li>\n<li>Multiple integrals<\/li>\n<li>Sums<\/li>\n<li>Pattern recognition<\/li>\n<li>Common sense and checking answers<\/li>\n<\/ul>\n<p><strong>B R Programming<\/strong><\/p>\n<ul>\n<li>Vectors<\/li>\n<li>Matrices<\/li>\n<li>Math<\/li>\n<li>Sampling and simulation<\/li>\n<li>Plotting<\/li>\n<li>Programming<\/li>\n<li>Summary statistics<\/li>\n<li>Distributions<\/li>\n<\/ul>\n<p><strong>C Table of distributions<\/strong><\/p>\n<p><strong>Bibliography<\/strong><\/p>\n<p><strong>Index<\/strong><\/p>\n<\/p>\n<\/div>\n<p><a href=\"https:\/\/www.datasciencecentral.com\/xn\/detail\/6448529:BlogPost:829629\">Go to Source<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Author: Capri Granville A free online version of the second edition of the book based on Stat 110,\u00a0Introduction to Probability\u00a0by Joe Blitzstein and Jessica Hwang,\u00a0is [&hellip;] <span class=\"read-more-link\"><a class=\"read-more\" href=\"https:\/\/www.aiproblog.com\/index.php\/2019\/05\/24\/free-textbook-probability-course-harvard-university-based-on-r\/\">Read More<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":458,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[26],"tags":[],"_links":{"self":[{"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/posts\/2183"}],"collection":[{"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/comments?post=2183"}],"version-history":[{"count":0,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/posts\/2183\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/media\/456"}],"wp:attachment":[{"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/media?parent=2183"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/categories?post=2183"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.aiproblog.com\/index.php\/wp-json\/wp\/v2\/tags?post=2183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}