{"id":1122,"date":"2025-02-02T08:20:25","date_gmt":"2025-02-02T16:20:25","guid":{"rendered":"https:\/\/dornsife.usc.edu\/larry-goldstein\/?page_id=1122"},"modified":"2025-06-11T13:05:23","modified_gmt":"2025-06-11T20:05:23","slug":"1122-2","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/larry-goldstein\/1122-2\/","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 style=\"text-align: center;\"><strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0Probability Theory: Math 407, Spring 2025<\/strong><\/h2>\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>26% Midterm exam, Wednesday, May 28th<\/li>\n<li>35% Final Exam, June 13th<\/li>\n<li>24% Three Quizzes, one on the first Thursdays during 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><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/AdditionalProblems.pdf\">Additional Problems<\/a><\/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: 3,5,11,12,15,20,23,28,32,35,36,41,44,49,50,51,52,53,54,56<\/p>\n<p>&nbsp;<\/p>\n<p>Chapter 5: 2,5,7,9,10,16,18,20,21,22,24,28,31,33,37,38, 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: 4, 12, 13, 15, 18<\/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 conditions on the behavior of E[T_n]),27*, 29*, 32*, 33* (*=optional)<\/p>\n<p><a href=\"https:\/\/www.appstate.edu\/~steelekm\/classes\/psy2510\/birthtable.html\">Birthday Probability Table<\/a><\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Monty_Hall_problem\">Monty Hall Problem<\/a><\/p>\n<p><strong>Class Notes<\/strong>:<\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/2025-05-19_08.35.pdf\">19 May<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/2025-05-20_09.43.pdf\">20 May<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/2025-05-21_08.51.pdf\">21 May<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/2025-05-22_09.56.pdf\">22 May<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/2025-05-23_08.53.pdf\">23 May<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/2025-05-26_09.00.pdf\">26 May<\/a><\/p>\n<p>27 May <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/2025-05-27_10.49-1.pdf\">a<\/a>) <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/2025-05-27_12.07-1.pdf\">b<\/a>)<\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/2025-05-28_09.02a.pdf\">28 May<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/2025-05-29_09.45-1.pdf\">29 May<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/06\/2025-06-03_09.48.pdf\">3 June<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/06\/2025-06-04_09.02.pdf\">4 June<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/06\/2025-06-05_09.48.pdf\">5 June<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/06\/2025-06-06_08.53.pdf\">6 June<\/a><\/p>\n<p>9 June<\/p>\n<p>10 June <a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/06\/2025-06-10_09.42.pdf\">a)<\/a>\u00a0<a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/06\/2025-06-10_13.00.pdf\">b)<\/a><\/p>\n<p>11 June<\/p>\n<p>Exercise Sheets<\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/Ex1.pdf\">Ex. 1<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/Ex2.pdf\">Ex. 2<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/05\/Ex3-no-sol.pdf\">Ex. 3<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/06\/Ex4.pdf\">Ex.4<\/a><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2025\/06\/Ex5-no-sol.pdf\">Ex.5<\/a><\/p>\n<p>&nbsp;<\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":396,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1122","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, 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