{"id":109147,"date":"2023-11-12T14:16:00","date_gmt":"2023-11-12T06:16:00","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=109147"},"modified":"2026-08-04T11:06:52","modified_gmt":"2026-08-04T03:06:52","slug":"%e9%80%9a%e8%a8%8a%e9%ab%98%e7%ad%89%e6%a9%9f%e7%8e%87-advanced-probability-for-communications-109%e5%ad%b8%e5%b9%b4%e5%ba%a6-%e9%9b%bb%e6%a9%9f%e5%b7%a5%e7%a8%8b%e5%ad%b8%e7%b3%bb-%e9%99%b3","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course\/college-of-electrical-and-computer-engineering\/%e9%80%9a%e8%a8%8a%e9%ab%98%e7%ad%89%e6%a9%9f%e7%8e%87-advanced-probability-for-communications-109%e5%ad%b8%e5%b9%b4%e5%ba%a6-%e9%9b%bb%e6%a9%9f%e5%b7%a5%e7%a8%8b%e5%ad%b8%e7%b3%bb-%e9%99%b3","title":{"rendered":"\u901a\u8a0a\u9ad8\u7b49\u6a5f\u7387 Advanced Probability for Communications &#8211; 109\u5b78\u5e74\u5ea6 | \u96fb\u6a5f\u5de5\u7a0b\u5b78\u7cfb \u9673\u4f2f\u5be7\u8001\u5e2b"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"109147\" class=\"elementor elementor-109147\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-top-section elementor-element elementor-element-90a0113 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"90a0113\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-100 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-78bf394\" data-id=\"78bf394\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-20 elementor-section elementor-top-section elementor-element elementor-element-0025485 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0025485\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-0446ed9\" data-id=\"0446ed9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2f5840a elementor-widget elementor-widget-penci-info-box\" data-id=\"2f5840a\" data-element_type=\"widget\" data-widget_type=\"penci-info-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"penci_info_box_69514\" class=\"penci-block-vc penci-info-box penci-ibox-float-left penci-view-default penci-shape-circle\">\r\n\t\t\t<div class=\"penci-ibox-inner\">\r\n\t\t\t\t\t\t\t\t<div class=\"penci-ibox-icon penci-ibox-icon--icon penci-icon penci-tibox-text\"><span class=\"penci-ibox-icon-fa\"><\/span><\/div>\t\t\t\t<div class=\"penci-ibox-content-wrap\">\r\n\t\t\t\t\t<div class=\"penci-ibox-stit\">Advanced Probability for Communications - 109 Academic Year<\/div>\t\t\t\t\t<h3 class=\"penci-ibox-title\">\u901a\u8a0a\u9ad8\u7b49\u6a5f\u7387 - 109\u5b78\u5e74\u5ea6<\/h3>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c6381f4 elementor-widget elementor-widget-eael-adv-tabs\" data-id=\"c6381f4\" data-element_type=\"widget\" data-widget_type=\"eael-adv-tabs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t        <div id=\"eael-advance-tabs-c6381f4\" class=\"eael-advance-tabs eael-tabs-horizontal eael-tab-auto-active\" data-tabid=\"c6381f4\">\n            <div class=\"eael-tabs-nav\">\n                <ul class=\"eael-tab-inline-icon\">\n                                            <li id=\"home\" class=\"active-default eael-tab-item-trigger\" aria-selected=\"true\" data-tab=\"1\" role=\"tab\" tabindex=\"0\" aria-controls=\"home-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-fas-home\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M280.37 148.26L96 300.11V464a16 16 0 0 0 16 16l112.06-.29a16 16 0 0 0 15.92-16V368a16 16 0 0 1 16-16h64a16 16 0 0 1 16 16v95.64a16 16 0 0 0 16 16.05L464 480a16 16 0 0 0 16-16V300L295.67 148.26a12.19 12.19 0 0 0-15.3 0zM571.6 251.47L488 182.56V44.05a12 12 0 0 0-12-12h-56a12 12 0 0 0-12 12v72.61L318.47 43a48 48 0 0 0-61 0L4.34 251.47a12 12 0 0 0-1.6 16.9l25.5 31A12 12 0 0 0 45.15 301l235.22-193.74a12.19 12.19 0 0 1 15.3 0L530.9 301a12 12 0 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aria-controls=\"calendar-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-far-calendar-alt\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M148 288h-40c-6.6 0-12-5.4-12-12v-40c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12zm108-12v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm96 0v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm-96 96v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm-96 0v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm192 0v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm96-260v352c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V112c0-26.5 21.5-48 48-48h48V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 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24-24v-16c0-7.5-3.5-14.3-8.9-18.7-4.2-15.4-4.2-59.3 0-74.7 5.4-4.3 8.9-11.1 8.9-18.6zM128 134c0-3.3 2.7-6 6-6h212c3.3 0 6 2.7 6 6v20c0 3.3-2.7 6-6 6H134c-3.3 0-6-2.7-6-6v-20zm0 64c0-3.3 2.7-6 6-6h212c3.3 0 6 2.7 6 6v20c0 3.3-2.7 6-6 6H134c-3.3 0-6-2.7-6-6v-20zm253.4 250H96c-17.7 0-32-14.3-32-32 0-17.6 14.4-32 32-32h285.4c-1.9 17.1-1.9 46.9 0 64z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">\u8ab2\u7a0b\u8b1b\u7fa9<\/span>                            \n                                                    <\/li>\n                                    <\/ul>\n            <\/div>\n            \n            <div class=\"eael-tabs-content\">\n\t\t        \n                    <div id=\"home-tab\" class=\"clearfix eael-tab-content-item active-default\" data-title-link=\"home-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><style type=\"text\/css\">\n.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/><\/style><\/p><p style=\"margin-bottom: 10px; line-height: 28px; color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u672c\u8ab2\u7a0b\u662f\u7531\u00a0<a href=\"https:\/\/ece.nycu.edu.tw\/\" target=\"_blank\" rel=\"noopener\">\u570b\u7acb\u967d\u660e\u4ea4\u901a\u5927\u5b78\u96fb\u6a5f\u5de5\u7a0b\u5b78\u7cfb <\/a>\u63d0\u4f9b\u3002<\/p><p class=\"text\">This course intends to provide students with the necessary background on advanced probability theories for communications. It is our hope that students, after taking this course, are capable of self-reading\u00a0 papers in communications. Enhancing students' capability for theoretical research is another objective of this course.<\/p><p>\u00a0<\/p><p class=\"text\">Accordingly, not only proofs for theories will be introduced in detail, but also their implications in communications will be stated in lectures. Students who take this course are recommended to have certain knowledge on fundamental probabilistic theories.<\/p><p>\u00a0<\/p><p><span style=\"color: #3366ff; font-size: 16px;\">\u8ab2\u7a0b\u7528\u66f8\uff1a<\/span><\/p><p class=\"text\">Lecture notes<\/p><p style=\"color: #ff00ff; font-size: 14px;\">\u70ba\u6c42\u5b78\u7fd2\u6210\u6548\u5b8c\u7f8e\uff0c\u8acb\u8cfc\u8cb7\u8ab2\u672c\uff01<\/p><p>\u00a0<\/p><table style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\" border=\"1\"><tbody><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\" width=\"100\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u6388\u8ab2\u6559\u5e2b<\/span><\/span><\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0\u96fb\u6a5f\u5de5\u7a0b\u5b78\u7cfb \u9673\u4f2f\u5be7\u8001\u5e2b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u8ab2\u7a0b\u5b78\u5206<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a03\u5b78\u5206<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th class=\"text\" style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u6388\u8ab2\u5e74\u5ea6<\/span><\/span><\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0109\u5b78\u5e74\u5ea6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u6388\u8ab2\u5c0d\u8c61<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0\u78a9\u58eb\u73ed<br \/><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u9810\u5099\u77e5\u8b58<\/span><\/span><\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0\u6a5f\u7387<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u8ab2\u7a0b\u63d0\u4f9b<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0<a href=\"#video\">\u8ab2\u7a0b\u5f71\u97f3<\/a>\u00a0 \u00a0<a href=\"#syllabus\">\u8ab2\u7a0b\u7db1\u8981<\/a> \u00a0\u00a0<a href=\"#calendar\">\u8ab2\u7a0b\u884c\u4e8b\u66c6<\/a> \u00a0\u00a0<a href=\"#handout\">\u8ab2\u7a0b\u8b1b\u7fa9<\/a>\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"video-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"video-tab\">\n\t\t\t\t        \t\t\t\t\t        <p>\n<table id=\"tablepress-505\" class=\"tablepress tablepress-id-505\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">\u9031\u6b21<\/th><th class=\"column-2\">\u8ab2\u7a0b\u5167\u5bb9<\/th><th class=\"column-3\">\u8ab2\u7a0b\u5f71\u97f3<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec01 The Law of Large Numbers<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109177\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec02 Large Deviations and The Law of The Iterated Logarithm<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109211\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec03 Large Deviations and The Law of The Iterated Logarithm<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109217\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec04 Random Variables and Distributions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109225\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec05 Random Variables and Distributions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109231\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec06 Random Variables and Distributions, Expected Values<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109237\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec07 Sums of Independent Random Variables, Convergence of Distributions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109245\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec08 Convergence of Distributions, Characteristic Functions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109251\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec09 Characteristic Functions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109259\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec10 Characteristic Functions, The Central Limit Theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109269\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec11 The Central Limit Theorem, Infinitely Divisible Distributions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109275\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec12 Infinitely Divisible Distributions, Ninness\u2019s Strong Law of Large Numbers, Brownian Motion, Berry-Esseen Theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109281\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec13 Berry-Esseen Theorem, Basic Order Statistics, Basic Theories On Order Statistics<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109287\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Lec14 Basic Theories On Order Statistics, Order Statistics of Cumulative Sums, Induced Order Statistics<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=109293\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-505 from cache -->\u00a0<\/p>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"syllabus-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"syllabus-tab\">\n\t\t\t\t        \t\t\t\t\t        <p class=\"title\"><strong>\u8ab2\u7a0b\u76ee\u6a19<\/strong><\/p><p class=\"text\">This course intends to provide students with the necessary background on advanced probability theories for communications. It is our hope that students, after taking this course, are capable of self-reading papers in communications. Enhancing students' capability for theoretical research is another objective of this course.<\/p><p class=\"text\">Accordingly, not only proofs for theories will be introduced in detail, but also their implications in communications will be stated in lectures. Students who take this course are recommended to have certain knowledge on fundamental probabilistic theories.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u7ae0\u7bc0<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong> \u55ae\u5143\u4e3b\u984c<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong> \u5167\u5bb9\u7db1\u8981<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e00<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Law of large numbers (including the strong law, and the weak law), Borel-Cantelli lemmas<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u4e8c<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Large deviations, the law of the iterated logarithm, moment generating functions versus large deviations, Chernoff's theorem<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e09<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\"> Random variables, convergence in probabilities.<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u56db<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Characterization of relation between expectation values and<br \/>(1) limits,<br \/>(2) distributions,<br \/>(3) moments.<br \/>Several inequalities regarding expectation values will also be covered.<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e94<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Sums of independent random variables, and their relation with the strong\/weak law and moment generating functions. Komogrov's zero-one law and maximal inequality will also be covered.<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u516d<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\"> Weak convergence in distributions.<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e03<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Characteristic functions inversion, uniqueness theorem, the continuity theorem.<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u516b<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">The central limit theorem, Lindeberg and Lyapounov theorems.<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e5d<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Infinitely divisible distributions.<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u5341<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\"> Brownian Motion.<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u5341\u4e00<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Derivation of error probability for Differential BPSK<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u5341\u4e8c<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Berry-Esseen Theorem<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u5341\u4e09<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Ordered statistics<\/span><\/td><\/tr><\/tbody><\/table><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u66f8\u76ee<\/strong><\/p><p class=\"text\">Lecture notes<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8a55\u5206\u6a19\u6e96<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong>\u9805\u76ee<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong>\u767e\u5206\u6bd4<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Study Report<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">50%<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Final Exam<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">50%<\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"calendar-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"calendar-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><span style=\"font-family: \u65b0\u7d30\u660e\u9ad4; font-size: 15px;\">\u672c\u8ab2\u7a0b\u884c\u4e8b\u66c6\u63d0\u4f9b\u8ab2\u7a0b\u9032\u5ea6\u8207\u8003\u8a66\u8cc7\u8a0a\u53c3\u8003\u3002<\/span><\/p><table style=\"font-style: normal; line-height: 20px; font-size: 15px; text-align: center;\" border=\"1\" cellspacing=\"0\"><tbody><tr><td bgcolor=\"#e4d8b0\" width=\"76\"><div style=\"text-align: center;\"><span style=\"color: #000000; font-weight: bold;\"><strong>\u5b78\u671f\u9031\u6b21<\/strong><\/span><\/div><\/td><td bgcolor=\"#e4d8b0\" width=\"135\"><div style=\"text-align: center;\" align=\"center\"><span style=\"font-family: 'Times New Roman'; font-weight: bold;\"><strong>\u4e0a\u8ab2\u65e5\u671f<\/strong><\/span><\/div><\/td><td bgcolor=\"#e4d8b0\" width=\"440\"><div style=\"text-align: center; font-size: 15px; font-weight: bold;\"><strong>\u53c3\u8003\u8ab2\u7a0b\u9032\u5ea6<\/strong><\/div><\/td><\/tr><tr><td style=\"text-align: center;\"><p><span class=\"text\">\u7b2c\u4e00\u9031<\/span><\/p><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\">2020\/09\/19<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>Law of large numbers (including the strong law, and the weak law), Borel-Cantelli lemmas<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u4e8c\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2020\/09\/26<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>Large deviations, the law of the iterated logarithm, moment generating functions versus large deviations, Chernoff's theorem<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e09\u9031<\/span><\/td><td style=\"text-align: center;\">2020\/10\/03<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>Large deviations, the law of the iterated logarithm, moment generating functions versus large deviations, Chernoff's theorem\u3000<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u56db\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2020\/10\/10<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>Holiday<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e94\u9031<\/span><\/td><td style=\"text-align: center;\">2020\/10\/17<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>Random variables, convergence in probabilities.<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u516d\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2020\/10\/24<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>Characterization of relation between expectation values and (1) limits, (2) distributions, (3) moments. Several inequalities regarding expectation values will also be covered.<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e03\u9031<\/span><\/td><td style=\"text-align: center;\">2020\/10\/31<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>Characterization of relation between expectation values and (1) limits, (2) distributions, (3) moments. Several inequalities regarding expectation values will also be covered.<\/li><li>\u00a0<\/li><li>Sums of independent random variables, and their relation with the strong\/weak law and moment generating functions. Komogrov's zero-one law and maximal inequality will also be covered.<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u516b\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2020\/11\/07<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>Weak convergence in distributions.<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e5d\u9031<\/span><\/td><td style=\"text-align: center;\">2020\/11\/14<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>Characteristic functions inversion, uniqueness theorem, the continuity theorem.<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2020\/11\/21<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#F2F2EC\"><ul><li>The central limit theorem, Lindeberg and Lyapounov theorems.<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e00\u9031<\/span><\/td><td style=\"text-align: center;\">2020\/11\/28<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>The central limit theorem, Lindeberg and Lyapounov theorems.<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u4e8c\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2020\/12\/05<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>Infinitely divisible distributions.<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e09\u9031<\/span><\/td><td style=\"text-align: center;\">2020\/12\/12<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>Brownian Motion.<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u56db\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\" bgcolor=\"#f2f2ec\">2020\/12\/19<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>Derivation of error probability for Differential BPSK<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e94\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\">2020\/12\/26<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>Berry-Esseen Theorem<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u516d\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\" bgcolor=\"#f2f2ec\">2021\/01\/02<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>Ordered statistics<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e03\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\">2021\/01\/09<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>Ordered statistics<\/li><\/ul><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"handout-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"handout-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><strong class=\"title\">\u8ab2\u7a0b\u8b1b\u7fa9 Course Handout<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td style=\"padding: 5px;\" bgcolor=\"#e4d8b0\"><strong> \u7ae0\u7bc0<\/strong><\/td><td style=\"padding: 5px;\" bgcolor=\"#e4d8b0\"><strong> \u4e0b\u8f09\u9023\u7d50<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Syllabus<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/1-syllabus20.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Section 6 The Law of Large Numbers<\/span><\/td><td style=\"padding: 5px; text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/2.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Section 9 Large Deviations and The Law of The Iterated Logarithm<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/3.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Section 20 Random Variables and Distributions<\/span><\/td><td style=\"padding: 5px; text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/4.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Section 21 Expected Values<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/5.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Section 22 Sums of Independent Random Variables<\/span><\/td><td style=\"padding: 5px; text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/6.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Section 25 Convergence of Distributions<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/7.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Section 26 Characteristic Functions<\/span><\/td><td style=\"padding: 5px; text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/8.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Section 27 The Central Limit Theorem<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/9.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Section 28 Infinitely Divisible Distributions<\/span><\/td><td style=\"padding: 5px; text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/10.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Ninness\u2019s Strong Law of Large Numbers<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/11.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Section 37 Brownian Motion<\/span><\/td><td style=\"padding: 5px; text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/12.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Berry-Esseen Theorem<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/13.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Basic Order Statistics<\/span><\/td><td style=\"padding: 5px; text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/14.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Basic Theories On Order Statistics<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/apfc091\/Handout\/15.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Order Statistics of Cumulative Sums<\/span><\/td><td style=\"padding: 5px; 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