{"id":780,"date":"2024-05-10T06:20:50","date_gmt":"2024-05-10T13:20:50","guid":{"rendered":"https:\/\/dornsife.usc.edu\/larry-goldstein\/?page_id=780"},"modified":"2025-02-02T08:21:21","modified_gmt":"2025-02-02T16:21:21","slug":"780-2","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/larry-goldstein\/teaching\/780-2\/","title":{"rendered":""},"content":{"rendered":"\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <h2><strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Probability Theory: Math 407<\/strong><\/h2>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Instructor:\u00a0<a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/\">Larry Goldstein<\/a>, <a href=\"mailto:larry@usc.edu\">larry@usc.edu<\/a><\/p>\n<p>Course Prerequisite: USC MATH 226 or MATH 227, or an equivalent advanced multivariate calculus course.<\/p>\n<p><strong>Text and Course Coverage<\/strong><\/p>\n<p>Introduction to Probability, by David Anderson, Timo Seppalainen, and Benedek Valko<\/p>\n<p>The course will cover the following material:<\/p>\n<p>Chapter 1: Experiments with random outcomes, Sections 1.1-1.5<\/p>\n<p>Chapter 2: Conditional probability and Independence, Sections 2.1-2.4<\/p>\n<p>Chapter 3: Random Variables: Sections 3.1-3.5<\/p>\n<p>Chapter 4: Approximations of the binomial distribution, Sections 4.1-4.6<\/p>\n<p>Chapter 5: Transforms and transformations, Sections 5.1-5.2<\/p>\n<p>Chapter 6: Joint distributions of random variables, Sections 6.2-6.3<\/p>\n<p>Chapter 9: Tail bounds and limit theorems, Sections 9.1-9.3<\/p>\n<p><strong>Exams and Grading Policy<\/strong><\/p>\n<ul>\n<li>15% Attendance<\/li>\n<li>25% Midterm exam, May 21st.<\/li>\n<li>35% Final Exam, June 7th,<\/li>\n<li>25% Four Quizzes, two on the first two Thursdays of the problem session, and the next two on the last two Tuesdays, covering the material since the previous quiz up to the Tuesday\/Friday of the week of the quiz.<\/li>\n<\/ul>\n<p><strong>Assignments <\/strong><\/p>\n<p>Chapter 1: 1,2,8,9,12,13,16,19,21,23,30,32,41,43,51,58,59<\/p>\n<p>&nbsp;<\/p>\n<p>Chapter 2: 2,5,9,11,14,19,21,22,31,34,48,67,85,88<\/p>\n<p>&nbsp;<\/p>\n<p>Chapter 3: 1,3,7,9,15,17,31,40,46,52,56,57,58,63,66,69,74,77<\/p>\n<p>&nbsp;<\/p>\n<p>Chapter 4: 3,5,11,12,15,20,23,28,32,35,36,41,44,49,50,52,53,54,56<\/p>\n<p>&nbsp;<\/p>\n<p>Chapter 5: 2,5,7,9,10,16,18,20,21,22,24,28,31,33,37,39,40,43<\/p>\n<p>&nbsp;<\/p>\n<p>Chapter 6: 7,13,15*,18,19,21,22,29,36,39,47,50*,55,57,58,60* (*=optional)<\/p>\n<p>&nbsp;<\/p>\n<p>Chapter 7: 7.4, 7.15<\/p>\n<p>&nbsp;<\/p>\n<p>Chapter 9: 2,4,17,20,21*,24*,25* (is the condition |Cov(X_i,X_{i+1})| \u2264c needed?), 26 (you may add additional conditional on the behavior of E[T_n]),27*, 29*, 32*, 33* (*=optional)<\/p>\n<p><strong>Class notes:\u00a0 May 13: <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/Screenshot1-2024-05-13-at-7.59.37\u202fPM.png\">1<\/a>, <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/Screenshot2-2024-05-13-at-8.00.15\u202fPM.png\">2<\/a>, <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/Screenshot3-2024-05-13-at-8.02.39\u202fPM.png\">3<\/a>, <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/Screenshot4-2024-05-13-at-8.03.07\u202fPM.png\">4<\/a>, <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/Screenshot5-2024-05-13-at-8.03.28\u202fPM.png\">5<\/a>, <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/Screenshot6-2024-05-13-at-8.03.51\u202fPM.png\">6<\/a>, <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/Screenshot7-2024-05-13-at-8.04.44\u202fPM.png\">7<\/a>, <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/Screenshot8-2024-05-13-at-8.05.03\u202fPM.png\">8<\/a><\/strong><\/p>\n<p><strong>\u00a0<a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-14_12-L.pdf\">May 14<\/a><\/strong><\/p>\n<p><strong>\u00a0<a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-14_14-PS.pdf\">May 14<\/a><\/strong><\/p>\n<p><strong>\u00a0<a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-15_12-L.pdf\">May 15<\/a><\/strong><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-16_12-L.pdf\"><strong>May 16<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-16_15-PS.pdf\"><strong>May 16<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-17_11-L.pdf\"><strong>May 17<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-20_12.pdf\"><strong>May 20<\/strong><\/a><\/p>\n<p><strong><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-21_12-L.pdf\">May 21<\/a><\/strong><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-22_L.pdf\"><strong>May 22<\/strong><\/a><\/p>\n<p><strong><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-23_PS.pdf\">May 23, problem session<\/a><\/strong><\/p>\n<p><strong><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-23_12L.pdf\">May 23<\/a><\/strong><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-27L-1.pdf\"><strong>May 27<\/strong><\/a><\/p>\n<p><strong><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-28_12L.pdf\">May 28<\/a><\/strong><\/p>\n<p><strong><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-29_12L.pdf\">May 29<\/a><\/strong><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/06\/2024-05-29PS.pdf\"><strong>May 29, problem session<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-30L.pdf\"><strong>May 30<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-30_14PS.pdf\"><strong>May 30<\/strong><\/a>, <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-30_14PS.pdf\">problem session<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/2024-05-31L.pdf\"><strong>May 31<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/06\/2024-06-03L.pdf\"><strong>June 3<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/06\/2024-06-04_12-09.pdf\"><strong>June 4, AM<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/06\/2024-06-04_14.pdf\"><strong>June 4, PM<\/strong><\/a><\/p>\n<p><strong>June 5 (too large for this page, uploaded to University (USC\/LUISS) specific site)<\/strong><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/06\/2024-06-06AM.pdf\"><strong>June 6, AM<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/06\/2024-06-06PM.pdf\"><strong>June 6, PM<\/strong><\/a><\/p>\n<p><strong>Exercises<\/strong>: <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/Ex1_sol.pdf\">1,<\/a><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/Ex2_sol.pdf\">2, <\/a><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/AdditionalExercises_1.pdf\">Additional Exercises<\/a>, <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/Ex3.pdf\">3,\u00a0<\/a><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/06\/Ex4.pdf\">4, <\/a><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/06\/Ex5-no-sol.pdf\">5<\/a><\/p>\n<p><strong><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2024\/05\/AppliedProblems.pdf\">Applied Problems<\/a><\/strong><\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":396,"featured_media":0,"parent":149,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-780","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>- Larry Goldstein<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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