{"id":271,"date":"2025-04-23T23:11:40","date_gmt":"2025-04-24T04:11:40","guid":{"rendered":"https:\/\/mathtalker.org\/blog\/?page_id=271"},"modified":"2026-04-16T16:12:50","modified_gmt":"2026-04-16T21:12:50","slug":"probability-theory-class-notes","status":"publish","type":"page","link":"https:\/\/mathtalker.org\/blog\/probability-theory-class-notes\/","title":{"rendered":"Probability Theory"},"content":{"rendered":"<p><script type=\"application\/ld+json\"><br \/>\n{<br \/>\n  \"@context\": \"https:\/\/schema.org\",<br \/>\n  \"@type\": \"CollectionPage\",<br \/>\n  \"name\": \"Probability Theory Class Notes\",<br \/>\n  \"headline\": \"Probability Theory Class Notes\",<br \/>\n  \"description\": \"Free probability theory class notes based on Blitzstein and Hwang, with worked examples, in-class activities, and solutions covering counting, conditional probability, random variables, expectation, joint distributions, and the central limit theorem.\",<br \/>\n  \"url\": \"https:\/\/mathtalker.org\/www\/classes\/probability.php\",<br \/>\n  \"author\": {<br \/>\n    \"@type\": \"Person\",<br \/>\n    \"name\": \"Jodin Morey\",<br \/>\n    \"url\": \"https:\/\/mathtalker.org\/www\/\"<br \/>\n  },<br \/>\n  \"publisher\": {<br \/>\n    \"@type\": \"Person\",<br \/>\n    \"name\": \"Jodin Morey\"<br \/>\n  },<br \/>\n  \"about\": [<br \/>\n    \"Probability theory\",<br \/>\n    \"Sample spaces\",<br \/>\n    \"Counting\",<br \/>\n    \"Conditional probability\",<br \/>\n    \"Bayes' rule\",<br \/>\n    \"Independence\",<br \/>\n    \"Random variables\",<br \/>\n    \"Distributions\",<br \/>\n    \"Expectation\",<br \/>\n    \"Variance\",<br \/>\n    \"Joint distributions\",<br \/>\n    \"Conditional expectation\",<br \/>\n    \"Central limit theorem\"<br \/>\n  ]<br \/>\n}<br \/>\n<\/script><\/p>\n<h2>Probability Theory Class Notes<\/h2>\n<p><strong>Keywords:<\/strong> probability theory notes, Blitzstein and Hwang, sample spaces, counting, conditional probability, Bayes rule, random variables, expectation, variance, conditional expectation, central limit theorem.<\/p>\n<p>As an instructor of introduction to probability theory, I prepared these PDFs as a review of the chapters in <a href=\"https:\/\/stat110.hsites.harvard.edu\/\" target=\"_blank\" rel=\"noopener noreferrer\"><em>Introduction to Probability<\/em> by Blitzstein and Hwang<\/a>. They include example problems which have been worked out in some detail. I hope you find these useful.<\/p>\n<style>\n.notes-table {<br \/>\n    width: 100%;<br \/>\n    border-collapse: collapse;<br \/>\n    margin-top: 20px;<br \/>\n}<\/p>\n<p>.notes-table th,<br \/>\n.notes-table td {<br \/>\n    border: 1px solid #999;<br \/>\n    padding: 10px;<br \/>\n    text-align: left;<br \/>\n    vertical-align: top;<br \/>\n}<\/p>\n<p>.notes-table th {<br \/>\n    background-color: #f2f2f2;<br \/>\n}<\/p>\n<p>.notes-table tr:nth-child(even) {<br \/>\n    background-color: #fafafa;<br \/>\n}<\/p>\n<p>.file-row {<br \/>\n    margin-bottom: 6px;<br \/>\n}<br \/>\n<\/style>\n<table class=\"notes-table\">\n<thead>\n<tr>\n<th>Class Notes<\/th>\n<th>In-Class Activities<\/th>\n<th>Solutions<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/01_Sec1p1_1p4_SampleSpace_NaiveDefinition_Counting_OverCounting.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.1 thru 1.4 Sample Space, Naive Definition, Counting, Over Counting<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_01_Ap1thru4.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 1.1\u20131.4<\/a><\/div>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_02_1p1_1p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 1.1\u20131.2<\/a><\/div>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_03_1p4.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 1.4<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_01_Ap1thru4_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 1.1\u20131.4<\/a><\/div>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_02_1p1_1p2_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 1.1\u20131.2<\/a><\/div>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_03_1p4_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 1.4<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/02_Sec1p5_1p6_Stories_NonNaive.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.5 1.6 Stories NonNaive<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_04_1p6.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 1.6<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_04_1p6_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 1.6<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/03_Sec2p1_Think_Conditionally.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.1 Think Conditionally<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_05a_2p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 2.1<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_05a_2p1_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 2.1<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/04_Sec2p2_2p3_2p4_ConditionallyProb_Bayes_LOTP.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.2 2.3 2.4 Conditional Probability, Bayes, LOTP<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_05_2p3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 2.3<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_05_2p3_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 2.3<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/05_Sec2p5_2p8_Independence_Coherency_ProblemSolving_PitfallsParadoxes.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.5 2.8 Independence, Coherency, Problem Solving, Pitfalls and Paradoxes<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_05b_2p5.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 2.5<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_05b_2p5_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 2.5<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/06_Sec3p1_3p2_RandomVariables_Distributions_ProbabilityMassFunctions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">3.1 3.2 Random Variables, Distributions, Probability Mass Functions<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/07_Sec3p3_3p5_Bernoulli_Binomial_Hypergeometric_Uniform.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">3.3 3.5 Bernoulli, Binomial, Hypergeometric, Uniform<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_06_3p3_3p5.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 3.3\u20133.5<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_06_3p3_3p5_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 3.3\u20133.5<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/08_Sec3p6_3p8_CumulativeDistributionFunctions_FunctionsOfRvs_Independence.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">3.6 3.8 Cumulative Distribution Functions, Functions of RVs, Independence<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_07_3p2_3p6_3p8.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 3.2, 3.6, 3.8<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_07_3p2_3p6_3p8_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 3.2, 3.6, 3.8<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/09_Sec4p1_4p3_Expectation_Linearity_Geometric_Negative_Binomial.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">4.1 4.3 Expectation, Linearity, Geometric, Negative Binomial<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_08_4p1_4p5.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 4.1, 4.5<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_08_4p1_4p5_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 4.1, 4.5<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/10_Sec4p5_4p6_LOTUS_Variance.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">4.5 4.6 LOTUS, Variance<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_09_4p6.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 4.6<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_09_4p6_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 4.6<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/11_Sec4p7_5p1_Poisson_ProbabilityDensityFunctions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">4.7 5.1 Poisson, Probability Density Functions<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_10_5p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 5.1<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_10_5p1_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 5.1<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/12_Sec5p2_5p3_Uniform_Universality.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">5.2 5.3 Uniform, Universality<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/13_Sec5p4_5p5_Normal_Exponential.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">5.4 5.5 Normal, Exponential<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_11_5p4_5p5.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 5.4\u20135.5<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_11_5p4_5p5_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 5.4\u20135.5<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/14_Sec6p1_6p3_DistributionSummaries_Moments_SampleMoments.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">6.1 6.3 Distribution Summaries, Moments, Sample Moments<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_12_6p1_6p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 6.1\u20136.2<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_12_6p1_6p2_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 6.1\u20136.2<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/15_Sec6p4_MomentGeneratingFunctions.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">6.4 Moment Generating Functions<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_13_6p2_thru_6p4.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 6.2\u20136.4<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_13_6p2_thru_6p4_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 6.2\u20136.4<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/16_Sec7p1_7p2_JointMarginalConditional_2DLOTUS.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">7.1 7.2 Joint Marginal, Conditional, 2D LOTUS<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_14_7p1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 7.1<\/a><\/div>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_15_7p1b.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 7.1<\/a><\/div>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_17_7p1_7p2_9p2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 7.1, 7.2, 9.2<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_14_7p1_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 7.1<\/a><\/div>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_15_7p1b_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 7.1<\/a><\/div>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_17_7p1_7p2_9p2_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 7.1, 7.2, 9.2<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/17_Sec8p1_ChangeOfVariables.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">8.1 Change of Variables<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/18_Sec9p1_9p2_ConditionalExpectation.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">9.1 9.2 Conditional Expectation<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/19_Sec7p3_Covariance_Correlation.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">7.3 Covariance Correlation<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_16_7p3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 7.3<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_16_7p3_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 7.3<\/a><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/20_Sec10p1_10p2_Inequalities_LawOfLargeNumbers.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">10.1 10.2 Inequalities, Law of Large Numbers<\/a><\/td>\n<td>\u2014<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/21_Sec10p3_CentralLimitTheorem.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">10.3 Central Limit Theorem<\/a><\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_18_9p3_thru_9p6.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 9.3\u20139.6<\/a><\/div>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_19_10p3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Activity 10.3<\/a><\/div>\n<\/td>\n<td>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_18_9p3_thru_9p6_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 9.3\u20139.6<\/a><\/div>\n<div class=\"file-row\"><a href=\"https:\/\/mathtalker.org\/www\/classes\/probabilitytheory_pdfs\/exercises\/Activity_19_10p3_Solns.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Solutions 10.3<\/a><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Probability Theory Class Notes Keywords: probability theory notes, Blitzstein and Hwang, sample spaces, counting, conditional probability, Bayes rule, random variables, expectation, variance, conditional expectation, central limit theorem. As an instructor of introduction to probability theory, I prepared these PDFs as &hellip; <a href=\"https:\/\/mathtalker.org\/blog\/probability-theory-class-notes\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"jetpack_post_was_ever_published":false,"footnotes":""},"class_list":["post-271","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Probability Theory - MathTalker<\/title>\n<meta name=\"description\" content=\"Free probability theory class notes based on Blitzstein and Hwang, with worked examples, in-class activities, and solutions covering counting, conditional probability, random variables, expectation, joint distributions, and the central limit theorem.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathtalker.org\/blog\/probability-theory-class-notes\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Probability Theory - 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