{"id":305,"date":"2018-12-20T07:13:09","date_gmt":"2018-12-20T07:13:09","guid":{"rendered":"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=305"},"modified":"2018-12-20T08:49:34","modified_gmt":"2018-12-20T08:49:34","slug":"probability-generating-functions","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/chapter\/probability-generating-functions\/","title":{"rendered":"Probability Generating Functions"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/_lMHCGvLPuM\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-306\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-74.png\" alt=\"\" width=\"497\" height=\"576\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-307\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-75.png\" alt=\"\" width=\"502\" height=\"693\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-308\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-76.png\" alt=\"\" width=\"515\" height=\"708\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-309\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-77.png\" alt=\"\" width=\"559\" height=\"714\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-310\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-78.png\" alt=\"\" width=\"530\" height=\"714\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-311\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-79.png\" alt=\"\" width=\"555\" height=\"565\" \/>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Probability Generating Functions<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/_lMHCGvLPuM\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\nReferences\r\n\r\n&nbsp;\r\n<ol>\r\n \t<li style=\"text-align: justify\">TM Apostol: Mathematical Analysis.<\/li>\r\n \t<li style=\"text-align: justify\">AK Basu: Measure Theory and Probability.<\/li>\r\n \t<li style=\"text-align: justify\">P Billingsley: Probability and Measure.<\/li>\r\n \t<li style=\"text-align: justify\">KL Chung: A Course in Probability Theory.<\/li>\r\n \t<li style=\"text-align: justify\">W Feller: An Introduction to Probability Theory and its Applications, Vol-I.<\/li>\r\n \t<li style=\"text-align: justify\">AM Gun, MK Gupta, B Dasgupta: An Outline of Statistical Theory, Vol -I.<\/li>\r\n \t<li style=\"text-align: justify\">E Luckacs, RG Laha: Applications of Characteristic Functions.<\/li>\r\n \t<li style=\"text-align: justify\">E Parzen: Modern Probability Theory and its Applications.<\/li>\r\n \t<li style=\"text-align: justify\">RJ Ser ing: Approximation Theorems of Mathematical Statistics.<\/li>\r\n \t<li style=\"text-align: justify\">W Rudin: Principles of Mathematical Analysis.<\/li>\r\n<\/ol>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/_lMHCGvLPuM\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-306\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-74.png\" alt=\"\" width=\"497\" height=\"576\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-74.png 497w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-74-259x300.png 259w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-74-65x75.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-74-225x261.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-74-350x406.png 350w\" sizes=\"auto, (max-width: 497px) 100vw, 497px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-307\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-75.png\" alt=\"\" width=\"502\" height=\"693\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-75.png 502w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-75-217x300.png 217w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-75-65x90.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-75-225x311.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-75-350x483.png 350w\" sizes=\"auto, (max-width: 502px) 100vw, 502px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-308\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-76.png\" alt=\"\" width=\"515\" height=\"708\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-76.png 515w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-76-218x300.png 218w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-76-65x89.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-76-225x309.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-76-350x481.png 350w\" sizes=\"auto, (max-width: 515px) 100vw, 515px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-309\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-77.png\" alt=\"\" width=\"559\" height=\"714\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-77.png 559w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-77-235x300.png 235w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-77-65x83.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-77-225x287.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-77-350x447.png 350w\" sizes=\"auto, (max-width: 559px) 100vw, 559px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-310\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-78.png\" alt=\"\" width=\"530\" height=\"714\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-78.png 530w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-78-223x300.png 223w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-78-65x88.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-78-225x303.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-78-350x472.png 350w\" sizes=\"auto, (max-width: 530px) 100vw, 530px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-311\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-79.png\" alt=\"\" width=\"555\" height=\"565\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-79.png 555w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-79-295x300.png 295w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-79-65x66.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-79-225x229.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-79-350x356.png 350w\" sizes=\"auto, (max-width: 555px) 100vw, 555px\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Probability Generating Functions<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/_lMHCGvLPuM\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>References<\/p>\n<p>&nbsp;<\/p>\n<ol>\n<li style=\"text-align: justify\">TM Apostol: Mathematical Analysis.<\/li>\n<li style=\"text-align: justify\">AK Basu: Measure Theory and Probability.<\/li>\n<li style=\"text-align: justify\">P Billingsley: Probability and Measure.<\/li>\n<li style=\"text-align: justify\">KL Chung: A Course in Probability Theory.<\/li>\n<li style=\"text-align: justify\">W Feller: An Introduction to Probability Theory and its Applications, Vol-I.<\/li>\n<li style=\"text-align: justify\">AM Gun, MK Gupta, B Dasgupta: An Outline of Statistical Theory, Vol -I.<\/li>\n<li style=\"text-align: justify\">E Luckacs, RG Laha: Applications of Characteristic Functions.<\/li>\n<li style=\"text-align: justify\">E Parzen: Modern Probability Theory and its Applications.<\/li>\n<li style=\"text-align: justify\">RJ Ser ing: Approximation Theorems of Mathematical Statistics.<\/li>\n<li style=\"text-align: justify\">W Rudin: Principles of Mathematical Analysis.<\/li>\n<\/ol>\n","protected":false},"author":3,"menu_order":18,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["mr-samopriya-basu"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-305","chapter","type-chapter","status-publish","hentry","contributor-mr-samopriya-basu"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/305","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":2,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/305\/revisions"}],"predecessor-version":[{"id":313,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/305\/revisions\/313"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/305\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/media?parent=305"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapter-type?post=305"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/contributor?post=305"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/license?post=305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}