{"id":383,"date":"2018-12-20T10:22:18","date_gmt":"2018-12-20T10:22:18","guid":{"rendered":"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=383"},"modified":"2018-12-20T10:23:02","modified_gmt":"2018-12-20T10:23:02","slug":"characteristic-functions-i","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/chapter\/characteristic-functions-i\/","title":{"rendered":"Characteristic Functions I"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/9sD-yGEBgJM\" 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&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-384\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-108.png\" alt=\"\" width=\"472\" height=\"499\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-385\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-109.png\" alt=\"\" width=\"497\" height=\"557\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-386\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-110.png\" alt=\"\" width=\"459\" height=\"585\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-387\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-111.png\" alt=\"\" width=\"459\" height=\"578\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-388\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-112.png\" alt=\"\" width=\"455\" height=\"578\" \/>\r\n\r\n&nbsp;\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Characteristic Functions I<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/9sD-yGEBgJM\" 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\nReferences\r\n<ol>\r\n \t<li>TM Apostol: Mathematical Analysis.<\/li>\r\n \t<li>AK Basu: Measure Theory and Probability.<\/li>\r\n \t<li>P Billingsley: Probability and Measure.<\/li>\r\n \t<li>KL Chung: A Course in Probability Theory.<\/li>\r\n \t<li>W Feller: An Introduction to Probability Theory and its Applications, Vol-I.<\/li>\r\n \t<li>AM Gun, MK Gupta, B Dasgupta: An Outline of Statistical Theory, Vol -I.<\/li>\r\n \t<li>E Luckacs, RG Laha: Applications of Characteristic Functions.<\/li>\r\n \t<li>E Parzen: Modern Probability Theory and its Applications.<\/li>\r\n \t<li>RJ Ser ing: Approximation Theorems of Mathematical Statistics.<\/li>\r\n \t<li>W Rudin: Principles of Mathematical Analysis<\/li>\r\n<\/ol>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/9sD-yGEBgJM\" 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>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-384\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-108.png\" alt=\"\" width=\"472\" height=\"499\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-108.png 472w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-108-284x300.png 284w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-108-65x69.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-108-225x238.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-108-350x370.png 350w\" sizes=\"auto, (max-width: 472px) 100vw, 472px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-385\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-109.png\" alt=\"\" width=\"497\" height=\"557\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-109.png 497w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-109-268x300.png 268w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-109-65x73.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-109-225x252.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-109-350x392.png 350w\" sizes=\"auto, (max-width: 497px) 100vw, 497px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-386\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-110.png\" alt=\"\" width=\"459\" height=\"585\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-110.png 459w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-110-235x300.png 235w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-110-65x83.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-110-225x287.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-110-350x446.png 350w\" sizes=\"auto, (max-width: 459px) 100vw, 459px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-387\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-111.png\" alt=\"\" width=\"459\" height=\"578\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-111.png 459w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-111-238x300.png 238w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-111-65x82.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-111-225x283.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-111-350x441.png 350w\" sizes=\"auto, (max-width: 459px) 100vw, 459px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-388\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-112.png\" alt=\"\" width=\"455\" height=\"578\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-112.png 455w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-112-236x300.png 236w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-112-65x83.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-112-225x286.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-112-350x445.png 350w\" sizes=\"auto, (max-width: 455px) 100vw, 455px\" \/><\/p>\n<p>&nbsp;<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Characteristic Functions I<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/9sD-yGEBgJM\" 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>References<\/p>\n<ol>\n<li>TM Apostol: Mathematical Analysis.<\/li>\n<li>AK Basu: Measure Theory and Probability.<\/li>\n<li>P Billingsley: Probability and Measure.<\/li>\n<li>KL Chung: A Course in Probability Theory.<\/li>\n<li>W Feller: An Introduction to Probability Theory and its Applications, Vol-I.<\/li>\n<li>AM Gun, MK Gupta, B Dasgupta: An Outline of Statistical Theory, Vol -I.<\/li>\n<li>E Luckacs, RG Laha: Applications of Characteristic Functions.<\/li>\n<li>E Parzen: Modern Probability Theory and its Applications.<\/li>\n<li>RJ Ser ing: Approximation Theorems of Mathematical Statistics.<\/li>\n<li>W Rudin: Principles of Mathematical Analysis<\/li>\n<\/ol>\n","protected":false},"author":3,"menu_order":26,"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-383","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\/383","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":1,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/383\/revisions"}],"predecessor-version":[{"id":389,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/383\/revisions\/389"}],"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\/383\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/media?parent=383"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapter-type?post=383"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/contributor?post=383"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/license?post=383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}